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9_NRSs_five_distribution_Weibull.R
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9_NRSs_five_distribution_Weibull.R
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#Copyright 2023 Tuban Lee
#These codes and manuscripts are under review in PNAS, please do not share them.
#If you are interested, please do not hesitate to contact me. Cooperation is also welcomed!
#require foreach and doparallel for parallel processing of bootstrap (not available for some types of computers)
if (!require("foreach")) install.packages("foreach")
library(foreach)
if (!require("doParallel")) install.packages("doParallel")
library(doParallel)
#require randtoolbox for random number generations
if (!require("randtoolbox")) install.packages("randtoolbox")
library(randtoolbox)
if (!require("Rcpp")) install.packages("Rcpp")
library(Rcpp)
if (!require("Rfast")) install.packages("Rfast")
library(Rfast)
if (!require("NRSReview")) install.packages("NRSReview_1.0.tar.gz", repos = NULL)
library(NRSReview)
if (!require("matrixStats")) install.packages("matrixStats")
library(matrixStats)
numCores <- detectCores()-4 # Detect the number of available cores
cl <- makeCluster(numCores) # Create a cluster with the number of cores
registerDoParallel(cl) # Register the parallel backend
asymptotic_n <- 331776*3*8
(asymptotic_n%%10)==0
# maximum order of moments
morder <- 4
#large sample size (asymptotic bias)
largesize<-331776*8
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol_asymptotic<-sobol(n=asymptotic_n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni_asymptotic<-rbind(quasiunisobol_asymptotic)
quasiunisobol_asymptotic<-c()
quasiuni_sorted2_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:2], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted3_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:3], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted4_asymptotic <- na.omit(rowSort(quasiuni_asymptotic, descend = FALSE, stable = FALSE, parallel = TRUE))
# Forever...
quasiuni_asymptotic<-Sort(sobol(n=largesize, dim = 1, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1))
orderlist1_AB2_asymptotic<-createorderlist(quni1=quasiuni_sorted2_asymptotic,size=largesize,interval=16,dimension=2)
orderlist1_AB2_asymptotic<-orderlist1_AB2_asymptotic[1:largesize,]
orderlist1_AB3_asymptotic<-createorderlist(quni1=quasiuni_sorted3_asymptotic,size=largesize,interval=16,dimension=3)
orderlist1_AB3_asymptotic<-orderlist1_AB3_asymptotic[1:largesize,]
orderlist1_AB4_asymptotic<-createorderlist(quni1=quasiuni_sorted4_asymptotic,size=largesize,interval=16,dimension=4)
orderlist1_AB4_asymptotic<-orderlist1_AB4_asymptotic[1:largesize,]
quasiuni_sorted2_asymptotic<-c()
quasiuni_sorted3_asymptotic<-c()
quasiuni_sorted4_asymptotic<-c()
asymptotic_n <- 331776*3*8
(asymptotic_n%%10)==0
# maximum order of moments
morder <- 6
#large sample size (asymptotic bias)
largesize<-331776*8
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol_asymptotic<-sobol(n=asymptotic_n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni_M<-rbind(quasiunisobol_asymptotic)
quasiunisobol_asymptotic<-c()
orderlist1_hllarge_asymptotic<-createorderlist(quni1=quasiuni_M[,1:6],size=largesize,interval=8,dimension=6)
orderlist1_hllarge_asymptotic<-orderlist1_hllarge_asymptotic[1:largesize,]
morder=6
unibatchran_M<-matrix(randtoolbox::SFMT(largesize*3*morder),ncol=morder)
orderlist1_hllarge_asymptotic_rand<-createorderlist(quni1=unibatchran_M[,1:6],size=largesize,interval=8,dimension=6)
orderlist1_hllarge_asymptotic_rand<-orderlist1_hllarge_asymptotic_rand[1:largesize,]
#load asymptotic d for two parameter distributions
d_values<- read.csv(("d_values.csv"))
I_values<- read.csv(("I_values.csv"))
Ismoments_values<- read.csv(("Ismoments_values.csv"))
Imoments_values<- read.csv(("Imoments_values.csv"))
#set the stop criterion
criterionset=1e-10
kurtWeibull<- read.csv(("kurtWeibull_31100.csv"))
allkurtWeibull<-unlist(kurtWeibull)
simulatedbatch_asymptoticbias<-foreach(batchnumber = (1:length(allkurtWeibull)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(randtoolbox)
library(NRSReview)
setSeed(1)
set.seed(1)
a=allkurtWeibull[batchnumber]
x<-c(dsWeibull(uni=quasiuni_asymptotic, shape=a/1, scale = 1))
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx, tol = 1e-10)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted=TRUE)
imoments1<-imoments(x=sortedx,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 5,releaseall=TRUE,standist_d=d_values,standist_I=I_values,standist_Ismoments=Ismoments_values,standist_Imoments=Imoments_values,orderlist1_sorted20=orderlist1_AB2_asymptotic,orderlist1_sorted30=orderlist1_AB3_asymptotic,orderlist1_sorted40=orderlist1_AB4_asymptotic,orderlist1_hlsmall=orderlist1_hllarge_asymptotic,orderlist1_hllarge=orderlist1_hllarge_asymptotic,percentage=1/24,batch="auto",stepsize=1000,criterion=1e-10,boot=TRUE)
imoments1<-unlist(imoments1)
momentsx<-standardizedmoments(x=sortedx,releaseall = TRUE)
#D Olive, Robust estimators for transformed location scale families. Unpubl. manuscript 1025 available from (www. math. siu. edu/olive/preprints. htm) (2006).
medianMAD1<-Weibull_median_MAD_estimator(sortedx)
#NB Marks, Estimation of weibull parameters from common percentiles. J. applied Stat. 32, 17–24 (2005).
QE1<-Weibull_quantile_estimator(x=sortedx,sorted=TRUE)
alpha1<-QE1[1]-0.3
alpha2<-QE1[1]+0.3
#X He, WK Fung, Method of medians for lifetime data with weibull models. Stat. medicine 18, 1993–2009 (1999)
RMLE1<-Weibull_RMLE(sortedx,alpha1=alpha1,alpha2=alpha2)
#all parameter setting are from
#K Boudt, D Caliskan, C Croux, Robust explicit estimators of weibull parameters. Metrika 73, 187–209 (2011).
moments_medianMAD1<-Weibull_moments(alpha=medianMAD1[1],lambda=medianMAD1[2])
moments_QE1<-Weibull_moments(alpha=QE1[1],lambda=QE1[2])
moments_RMLE1<-Weibull_moments(alpha=RMLE1[1],lambda=RMLE1[2])
MoM2<-median_of_means(sortedx,korder=2)
MoM3<-median_of_means(sortedx,korder=3)
MoM4<-median_of_means(sortedx,korder=4)
MoM5<-median_of_means(sortedx,korder=5)
MoM6<-median_of_means(sortedx,korder=6)
MoRMall<-mHLM_all(x=sortedx,max_dim=6,orderlists=orderlist1_hllarge_asymptotic_rand,boot=TRUE,quasi=FALSE,largesize=largesize)
MoRMall<-unlist(MoRMall)
sortedx<-c()
momentssd<-c(sd=sqrt(momentsx[2]),imoments1[3899],imoments1[3900],imoments1[3901])
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)-targetm)/sqrt(targetvar),
secondbias=abs(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])-targetvar)/momentssd[2],
thirdbias=abs(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])-targettm)/momentssd[3],
fourbias=abs(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])-targetfm)/momentssd[4],
skewbias=abs(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])-skewx),
kurtbias=abs(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902])-kurtx)
)
allrawmo1<-c(first=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)),
second=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])),
third=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])),
fourth=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])),
skew=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])),
kurt=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902]))
)
medianmoments<-c(imoments1[3706],imoments1[3780],imoments1[3834],imoments1[3875])
standardizedm<-c(imoments1[3706]/sqrt(targetvar),imoments1[3780]/momentssd[2],imoments1[3834]/momentssd[3],imoments1[3875]/momentssd[4])
all1<-(c(kurtx=kurtx,skewx=skewx,momentsx,allrawmoBias,momentssd,medianmoments,standardizedm=standardizedm,allrawmo1,Huberx,SMWM9,imoments1,targetall))
}
write.csv(simulatedbatch_asymptoticbias,paste("asymptotic_Weibull_raw_Process",largesize,".csv", sep = ","), row.names = FALSE)
#bootsize for bootstrap approximation of the distributions of the kernel of U-statistics.
n <- 13824*2*3
(n%%10)==0
# maximum order of moments
morder <- 4
#large sample size (approximating asymptotic)
largesize1<-13824*2
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol<-sobol(n=n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni<-quasiunisobol
quasiuni_sorted2 <- na.omit(rowSort(quasiuni[,1:2], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted3 <- na.omit(rowSort(quasiuni[,1:3], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted4 <- na.omit(rowSort(quasiuni, descend = FALSE, stable = FALSE, parallel = TRUE))
# Forever...
largesize1<-13824*2
samplesize=576*9
batchsizebase=1000
orderlist1_AB20<-createorderlist(quni1=quasiuni_sorted2,size=samplesize,interval=8,dimension=2)
orderlist1_AB20<-orderlist1_AB20[1:largesize1,]
orderlist1_AB30<-createorderlist(quni1=quasiuni_sorted3,size=samplesize,interval=8,dimension=3)
orderlist1_AB30<-orderlist1_AB30[1:largesize1,]
orderlist1_AB40<-createorderlist(quni1=quasiuni_sorted4,size=samplesize,interval=8,dimension=4)
orderlist1_AB40<-orderlist1_AB40[1:largesize1,]
setSeed(1)
morder=6
quasiuni_M<-sobol(n=(largesize1*3*morder), dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
largesize1<-13824*2
samplesize=576*9
orderlist1_hlsmall<-createorderlist(quni1=quasiuni_M[,1:6],size=samplesize,interval=8,dimension=6)
orderlist1_hlsmall<-orderlist1_hlsmall[1:largesize1,]
orderlist1_hllarge<-createorderlist(quni1=quasiuni_M[,1:6],size=largesize1,interval=8,dimension=6)
orderlist1_hllarge<-orderlist1_hllarge[1:largesize1,]
morder=6
# unibatchran_M<-matrix(randtoolbox::SFMT(largesize1*3*morder),ncol=morder)
#
# orderlist1_hlsmall_rand<-createorderlist(quni1=unibatchran_M[,1:6],size=samplesize,interval=8,dimension=6)
# orderlist1_hlsmall_rand<-orderlist1_hlsmall_rand[1:largesize1,]
setSeed(1)
orderlist1_AB6_randomall<-c()
for(i in (1:batchsizebase)){
unibatchran_M<-matrix(randtoolbox::SFMT(largesize1*3*morder),ncol=morder)
orderlist1_AB6_random<-createorderlist(quni1=unibatchran_M[,1:6],size=samplesize,interval=8,dimension=6)
orderlist1_AB6_random<-orderlist1_AB6_random[1:largesize1,]
unibatchran_M<-c()
orderlist1_AB6_randomall<-cbind(orderlist1_AB6_randomall,orderlist1_AB6_random)
}
batchsize=batchsizebase
n <- samplesize
setSeed(1)
unibatchran<-matrix(SFMT(samplesize*batchsize),ncol=batchsize)
unibatch<-colSort(unibatchran, descend = FALSE, stable = FALSE, parallel = TRUE)
simulatedbatch_ABSE<-foreach(batchnumber =c((1:length(allkurtWeibull))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(randtoolbox)
library(NRSReview)
setSeed(1)
set.seed(1)
a=allkurtWeibull[batchnumber]
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<-c()
for (batch1 in c(1:batchsize)){
x<-c(dsWeibull(uni=unibatch[,batch1], shape=a/1, scale = 1))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx, tol = 1e-10)
SMWM9<-SWA9(x=sortedx,interval=9,batch=1,sorted=TRUE)
imoments1<-imoments(x=sortedx,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 5,releaseall=TRUE,standist_d=d_values,standist_I=I_values,standist_Ismoments=Ismoments_values,standist_Imoments=Imoments_values,orderlist1_sorted20=orderlist1_AB20,orderlist1_sorted30=orderlist1_AB30,orderlist1_sorted40=orderlist1_AB40,orderlist1_hlsmall=orderlist1_hlsmall,orderlist1_hllarge=orderlist1_hllarge,percentage=1/24,batch="auto",stepsize=1000,criterion=1e-10,boot=TRUE)
imoments1<-unlist(imoments1)
momentsx<-standardizedmoments(x=sortedx,releaseall = TRUE)
#D Olive, Robust estimators for transformed location scale families. Unpubl. manuscript 1025 available from (www. math. siu. edu/olive/preprints. htm) (2006).
medianMAD1<-Weibull_median_MAD_estimator(sortedx)
#NB Marks, Estimation of weibull parameters from common percentiles. J. applied Stat. 32, 17–24 (2005).
QE1<-Weibull_quantile_estimator(x=sortedx,sorted=TRUE)
alpha1<-QE1[1]-0.3
alpha2<-QE1[1]+0.3
#X He, WK Fung, Method of medians for lifetime data with weibull models. Stat. medicine 18, 1993–2009 (1999)
RMLE1<-Weibull_RMLE(sortedx,alpha1=alpha1,alpha2=alpha2)
#all parameter setting are from
#K Boudt, D Caliskan, C Croux, Robust explicit estimators of weibull parameters. Metrika 73, 187–209 (2011).
moments_medianMAD1<-Weibull_moments(alpha=medianMAD1[1],lambda=medianMAD1[2])
moments_QE1<-Weibull_moments(alpha=QE1[1],lambda=QE1[2])
moments_RMLE1<-Weibull_moments(alpha=RMLE1[1],lambda=RMLE1[2])
MoM2<-median_of_means(sortedx,korder=2)
MoM3<-median_of_means(sortedx,korder=3)
MoM4<-median_of_means(sortedx,korder=4)
MoM5<-median_of_means(sortedx,korder=5)
MoM6<-median_of_means(sortedx,korder=6)
MoRMall<-mHLM_all(x=sortedx,max_dim=6,orderlists=orderlist1_AB6_randomall[,(seq(from=1, to=6*batchsizebase,by=6)[batch1]):(seq(from=6, to=6*batchsizebase,by=6)[batch1])],boot=TRUE,quasi=FALSE,largesize=largesize1)
MoRMall<-unlist(MoRMall)
sortedx<-c()
momentssd<-c(sd=sqrt(momentsx[2]),imoments1[3899],imoments1[3900],imoments1[3901])
allrawmoBias<-c(
firstbias=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)-targetm),
secondbias=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])-targetvar),
thirdbias=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])-targettm),
fourbias=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])-targetfm),
skewbias=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])-skewx),
kurtbias=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902])-kurtx)
)
allrawmo1<-c(first=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)),
second=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])),
third=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])),
fourth=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])),
skew=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])),
kurt=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902]))
)
medianmoments<-c(imoments1[3706],imoments1[3780],imoments1[3834],imoments1[3875])
standardizedm<-c(imoments1[3706]/sqrt(targetvar),imoments1[3780]/momentssd[2],imoments1[3834]/momentssd[3],imoments1[3875]/momentssd[4])
all1<-(c(kurtx=kurtx,skewx=skewx,momentsx,allrawmoBias,momentssd,medianmoments,standardizedm=standardizedm,allrawmo1,Huberx,SMWM9,imoments1,targetall))
SEbataches<-rbind(SEbataches,all1)
}
write.csv(SEbataches,paste("Weibull_raw_ABSSE_finite",samplesize,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSE1_mean<-sqrt(colMeans((SEbataches[,11:786])^2))/sqrt(targetvar)
RMSE1_var<-sqrt(colMeans((SEbataches[,787:1339])^2))/simulatedbatch_asymptoticbias[batchnumber,3847]
RMSE1_tm<-sqrt(colMeans((SEbataches[,1340:1766])^2))/simulatedbatch_asymptoticbias[batchnumber,3848]
RMSE1_fm<-sqrt(colMeans((SEbataches[,1767:2067])^2))/simulatedbatch_asymptoticbias[batchnumber,3849]
RMSE1_skew<-sqrt(colMeans((SEbataches[,2068:3112])^2))
RMSE1_kurt<-sqrt(colMeans((SEbataches[,3113:3845])^2))
AB1_mean<-abs(colMeans((SEbataches[,11:786])))/sqrt(targetvar)
AB1_var<-abs(colMeans((SEbataches[,787:1339])))/simulatedbatch_asymptoticbias[batchnumber,3847]
AB1_tm<-abs(colMeans((SEbataches[,1340:1766])))/simulatedbatch_asymptoticbias[batchnumber,3848]
AB1_fm<-abs(colMeans((SEbataches[,1767:2067])))/simulatedbatch_asymptoticbias[batchnumber,3849]
AB1_skew<-abs(colMeans((SEbataches[,2068:3112])))
AB1_kurt<-abs(colMeans((SEbataches[,3113:3845])))
SEbatachesmean <- colMeans(SEbataches)
ratiomean1<-c(SEbatachesmean[3858:4633])/SEbatachesmean[4583]
meansd_unscaled1<-apply((SEbataches[1:batchsize,3858:4633]), 2, unbiasedsd)
mean_SE1<-meansd_unscaled1/sqrt(targetvar)
mean_SEbatachesmeanprocess<-t(t(SEbataches[1:batchsize,3858:4633])/ratiomean1)
meansd1<-apply((mean_SEbatachesmeanprocess), 2, unbiasedsd)
mean_SSE1<-meansd1/sqrt(targetvar)
ratiovar1<-SEbatachesmean[4634:5186]/SEbatachesmean[5156]
varsd_unscaled1<-apply((SEbataches[1:batchsize,4634:5186]), 2, unbiasedsd)
var_SE1<-varsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3847]
var_SEbatachesvarprocess<-(t(t(SEbataches[1:batchsize,4634:5186])/ratiovar1))
varsd1<-apply(var_SEbatachesvarprocess, 2, unbiasedsd)
var_SSE1<-varsd1/simulatedbatch_asymptoticbias[batchnumber,3847]
ratiotm1<-SEbatachesmean[5187:5613]/SEbatachesmean[5589]
tmsd_unscaled1<-apply((SEbataches[1:batchsize,5187:5613]), 2, unbiasedsd)
tm_SE1<-tmsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3848]
tm_SEbatachestmprocess<-(t(t(SEbataches[1:batchsize,5187:5613])/ratiotm1))
tmsd1<-apply(tm_SEbatachestmprocess, 2, unbiasedsd)
tm_SSE1<-tmsd1/simulatedbatch_asymptoticbias[batchnumber,3848]
ratiofm1<-SEbatachesmean[5614:5914]/SEbatachesmean[5896]
fmsd_unscaled1<-apply((SEbataches[1:batchsize,5614:5914]), 2, unbiasedsd)
fm_SE1<-fmsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3849]
fm_SEbatachesfmprocess<-(t(t(SEbataches[1:batchsize,5614:5914])/ratiofm1))
fmsd1<-apply(fm_SEbatachesfmprocess, 2, unbiasedsd)
fm_SSE1<-fmsd1/simulatedbatch_asymptoticbias[batchnumber,3849]
ratio_skew1<-SEbatachesmean[5915:6959]/SEbatachesmean[6959]
skewsd_unscaled1<-apply((SEbataches[1:batchsize,5915:6959]), 2, unbiasedsd)
skew_SE1<-skewsd_unscaled1
skew_SEbatachesskewprocess<-(t(t(SEbataches[1:batchsize,5915:6959])/ratio_skew1))
skewsd1<-apply(skew_SEbatachesskewprocess, 2, unbiasedsd)
skew_SSE1<-skewsd1
ratio_kurt1<-SEbatachesmean[6960:7692]/SEbatachesmean[7692]
kurtsd_unscaled1<-apply((SEbataches[1:batchsize,6960:7692]), 2, unbiasedsd)
kurt_SE1<-kurtsd_unscaled1
kurt_SEbatacheskurtprocess<-(t(t(SEbataches[1:batchsize,6960:7692])/ratio_kurt1))
kurtsd1<-apply(kurt_SEbatacheskurtprocess, 2, unbiasedsd)
kurt_SSE1<-kurtsd1
allSE<-c(mean_SE1=mean_SE1,SEbatachesmean[1],var_SE1=var_SE1,SEbatachesmean[1],tm_SE1=tm_SE1,SEbatachesmean[1],fm_SE1=fm_SE1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSE_unstan<-c(SEbatachesmean[1],meansd_unscaled1=meansd_unscaled1,SEbatachesmean[1],varsd_unscaled1=varsd_unscaled1,SEbatachesmean[1],
tmsd_unscaled1=tmsd_unscaled1,SEbatachesmean[1],fmsd_unscaled1=fmsd_unscaled1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSSE<-c(SEbatachesmean[1],mean_SSE1=mean_SSE1,SEbatachesmean[1],var_SSE1=var_SSE1,SEbatachesmean[1],
tm_SSE1=tm_SSE1,SEbatachesmean[1],fm_SSE1=fm_SSE1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allSSE_unstand<-c(SEbatachesmean[1],meansd1=meansd1,SEbatachesmean[1],varsd1=varsd1,SEbatachesmean[1],
tmsd1=tmsd1,SEbatachesmean[1],fmsd1=fmsd1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allErrors<-c(samplesize=samplesize,kurt=SEbatachesmean[1],skew=SEbatachesmean[2],RMSE1_mean=RMSE1_mean,RMSE1_var=RMSE1_var,RMSE1_tm=RMSE1_tm,RMSE1_fm=RMSE1_fm,RMSE1_skew=RMSE1_skew,RMSE1_kurt=RMSE1_kurt,AB1_mean=AB1_mean,AB1_var=AB1_var,AB1_tm=AB1_tm,AB1_fm=AB1_fm,AB1_skew=AB1_skew,AB1_kurt=AB1_kurt,allSE=allSE,allSSE=allSSE,allSE_unstan=allSE_unstan,allSSE_unstand=allSSE_unstand,SEbatachesmean=SEbatachesmean)
allErrors
}
write.csv(simulatedbatch_ABSE,paste("Weibull_ABSSE.csv", sep = ","), row.names = FALSE)
simulatedbatch_ABSE_SE<-foreach(batchnumber =c((1:length(allkurtWeibull))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(randtoolbox)
library(NRSReview)
setSeed(1)
set.seed(1)
a=allkurtWeibull[batchnumber]
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("Weibull_raw_ABSSE_finite",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
SEbatachesmean <- colMeans(SEbataches)
ratiomean1<-c(SEbatachesmean[3858:4633])/SEbatachesmean[4583]
meansd_unscaled1<-apply((SEbataches[1:batchsize,3858:4633]), 2, se_mean)
mean_SE1<-meansd_unscaled1/sqrt(targetvar)
mean_SEbatachesmeanprocess<-t(t(SEbataches[1:batchsize,3858:4633])/ratiomean1)
meansd1<-apply((mean_SEbatachesmeanprocess), 2, se_mean)
mean_SSE1<-meansd1/sqrt(targetvar)
ratiovar1<-SEbatachesmean[4634:5186]/SEbatachesmean[5156]
varsd_unscaled1<-apply((SEbataches[1:batchsize,4634:5186]), 2, se_mean)
var_SE1<-varsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3847]
var_SEbatachesvarprocess<-(t(t(SEbataches[1:batchsize,4634:5186])/ratiovar1))
varsd1<-apply(var_SEbatachesvarprocess, 2, se_mean)
var_SSE1<-varsd1/simulatedbatch_asymptoticbias[batchnumber,3847]
ratiotm1<-SEbatachesmean[5187:5613]/SEbatachesmean[5589]
tmsd_unscaled1<-apply((SEbataches[1:batchsize,5187:5613]), 2, se_mean)
tm_SE1<-tmsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3848]
tm_SEbatachestmprocess<-(t(t(SEbataches[1:batchsize,5187:5613])/ratiotm1))
tmsd1<-apply(tm_SEbatachestmprocess, 2, se_mean)
tm_SSE1<-tmsd1/simulatedbatch_asymptoticbias[batchnumber,3848]
ratiofm1<-SEbatachesmean[5614:5914]/SEbatachesmean[5896]
fmsd_unscaled1<-apply((SEbataches[1:batchsize,5614:5914]), 2, se_mean)
fm_SE1<-fmsd_unscaled1/simulatedbatch_asymptoticbias[batchnumber,3849]
fm_SEbatachesfmprocess<-(t(t(SEbataches[1:batchsize,5614:5914])/ratiofm1))
fmsd1<-apply(fm_SEbatachesfmprocess, 2, se_mean)
fm_SSE1<-fmsd1/simulatedbatch_asymptoticbias[batchnumber,3849]
ratio_skew1<-SEbatachesmean[5915:6959]/SEbatachesmean[6959]
skewsd_unscaled1<-apply((SEbataches[1:batchsize,5915:6959]), 2, se_mean)
skew_SE1<-skewsd_unscaled1
skew_SEbatachesskewprocess<-(t(t(SEbataches[1:batchsize,5915:6959])/ratio_skew1))
skewsd1<-apply(skew_SEbatachesskewprocess, 2, se_mean)
skew_SSE1<-skewsd1
ratio_kurt1<-SEbatachesmean[6960:7692]/SEbatachesmean[7692]
kurtsd_unscaled1<-apply((SEbataches[1:batchsize,6960:7692]), 2, se_mean)
kurt_SE1<-kurtsd_unscaled1
kurt_SEbatacheskurtprocess<-(t(t(SEbataches[1:batchsize,6960:7692])/ratio_kurt1))
kurtsd1<-apply(kurt_SEbatacheskurtprocess, 2, se_mean)
kurt_SSE1<-kurtsd1
allSE<-c(mean_SE1=mean_SE1,SEbatachesmean[1],var_SE1=var_SE1,SEbatachesmean[1],tm_SE1=tm_SE1,SEbatachesmean[1],fm_SE1=fm_SE1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSE_unstan<-c(SEbatachesmean[1],meansd_unscaled1=meansd_unscaled1,SEbatachesmean[1],varsd_unscaled1=varsd_unscaled1,SEbatachesmean[1],
tmsd_unscaled1=tmsd_unscaled1,SEbatachesmean[1],fmsd_unscaled1=fmsd_unscaled1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSSE<-c(SEbatachesmean[1],mean_SSE1=mean_SSE1,SEbatachesmean[1],var_SSE1=var_SSE1,SEbatachesmean[1],
tm_SSE1=tm_SSE1,SEbatachesmean[1],fm_SSE1=fm_SSE1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allSSE_unstand<-c(SEbatachesmean[1],meansd1=meansd1,SEbatachesmean[1],varsd1=varsd1,SEbatachesmean[1],
tmsd1=tmsd1,SEbatachesmean[1],fmsd1=fmsd1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
allErrors<-c(samplesize=samplesize,kurt=SEbatachesmean[1],skew=SEbatachesmean[2],se_mean=se_mean_all1,allSE=allSE,allSSE=allSSE,allSE_unstan=allSE_unstan,allSSE_unstand=allSSE_unstand,SEbatachesmean=SEbatachesmean)
allErrors
}
write.csv(simulatedbatch_ABSE_SE,paste("Weibull_ABSSE_error.csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte<-foreach(batchnumber =c((1:100)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
library(randtoolbox)
setSeed(1)
set.seed(1)
a=allkurtWeibull[60]
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-c(kurtx=targetfm/(targetvar^(4/2)))
skewx<-c(skewx=targettm/(targetvar^(3/2)))
#bootsize for bootstrap approximation of the distributions of the kernal of U-statistics.
n <- round(batchnumber*13824*2*3/100)
(n%%10)==0
# maximum order of moments
morder <- 4
#large sample size (approximating asymptotic)
largesize<-round(batchnumber*13824*2/100)
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol<-sobol(n=n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni<-quasiunisobol
quasiuni_sorted2 <- na.omit(rowSort(quasiuni[,1:2], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted3 <- na.omit(rowSort(quasiuni[,1:3], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted4 <- na.omit(rowSort(quasiuni, descend = FALSE, stable = FALSE, parallel = TRUE))
samplesize=576*9
orderlist1_AB20<-createorderlist(quni1=quasiuni_sorted2,size=samplesize,interval=16,dimension=2)
orderlist1_AB20<-orderlist1_AB20[1:largesize,]
orderlist1_AB30<-createorderlist(quni1=quasiuni_sorted3,size=samplesize,interval=16,dimension=3)
orderlist1_AB30<-orderlist1_AB30[1:largesize,]
orderlist1_AB40<-createorderlist(quni1=quasiuni_sorted4,size=samplesize,interval=16,dimension=4)
orderlist1_AB40<-orderlist1_AB40[1:largesize,]
morder=6
quasiuni_M<-sobol(n=(largesize*3*morder), dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
samplesize=576*9
orderlist1_hlsmall<-createorderlist(quni1=quasiuni_M[,1:6],size=samplesize,interval=8,dimension=6)
orderlist1_hlsmall<-orderlist1_hlsmall[1:largesize,]
orderlist1_hllarge<-createorderlist(quni1=quasiuni_M[,1:6],size=largesize,interval=8,dimension=6)
orderlist1_hllarge<-orderlist1_hllarge[1:largesize,]
SEbataches<-c()
for (batch1 in c(1:batchsize)){
x<-c(dsWeibull(uni=unibatch[,batch1], shape=a/1, scale = 1))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx, tol = 1e-10)
SMWM9<-SWA9(x=sortedx,interval=9,batch=1,sorted=TRUE)
imoments1<-imoments(x=sortedx,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 5,releaseall=TRUE,standist_d=d_values,standist_I=I_values,standist_Ismoments=Ismoments_values,standist_Imoments=Imoments_values,orderlist1_sorted20=orderlist1_AB20,orderlist1_sorted30=orderlist1_AB30,orderlist1_sorted40=orderlist1_AB40,orderlist1_hlsmall=orderlist1_hlsmall,orderlist1_hllarge=orderlist1_hllarge,percentage=1/24,batch="auto",stepsize=1000,criterion=1e-10,boot=TRUE)
imoments1<-unlist(imoments1)
momentsx<-standardizedmoments(x=sortedx,releaseall = TRUE)
#D Olive, Robust estimators for transformed location scale families. Unpubl. manuscript 1025 available from (www. math. siu. edu/olive/preprints. htm) (2006).
medianMAD1<-Weibull_median_MAD_estimator(sortedx)
#NB Marks, Estimation of weibull parameters from common percentiles. J. applied Stat. 32, 17–24 (2005).
QE1<-Weibull_quantile_estimator(x=sortedx,sorted=TRUE)
alpha1<-QE1[1]-0.3
alpha2<-QE1[1]+0.3
#X He, WK Fung, Method of medians for lifetime data with weibull models. Stat. medicine 18, 1993–2009 (1999)
RMLE1<-Weibull_RMLE(sortedx,alpha1=alpha1,alpha2=alpha2)
#all parameter setting are from
#K Boudt, D Caliskan, C Croux, Robust explicit estimators of weibull parameters. Metrika 73, 187–209 (2011).
moments_medianMAD1<-Weibull_moments(alpha=medianMAD1[1],lambda=medianMAD1[2])
moments_QE1<-Weibull_moments(alpha=QE1[1],lambda=QE1[2])
moments_RMLE1<-Weibull_moments(alpha=RMLE1[1],lambda=RMLE1[2])
MoM2<-median_of_means(sortedx,korder=2)
MoM3<-median_of_means(sortedx,korder=3)
MoM4<-median_of_means(sortedx,korder=4)
MoM5<-median_of_means(sortedx,korder=5)
MoM6<-median_of_means(sortedx,korder=6)
MoRMall<-mHLM_all(x=sortedx,max_dim=6,boot=TRUE,quasi=FALSE,largesize=largesize)
MoRMall<-unlist(MoRMall)
sortedx<-c()
momentssd<-c(sd=sqrt(momentsx[2]),imoments1[3899],imoments1[3900],imoments1[3901])
allrawmoBias<-c(
firstbias=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)-targetm),
secondbias=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])-targetvar),
thirdbias=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])-targettm),
fourbias=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])-targetfm),
skewbias=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])-skewx),
kurtbias=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902])-kurtx)
)
allrawmo1<-c(first=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)),
second=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])),
third=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])),
fourth=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])),
skew=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])),
kurt=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902]))
)
medianmoments<-c(imoments1[3706],imoments1[3780],imoments1[3834],imoments1[3875])
standardizedm<-c(imoments1[3706]/sqrt(targetvar),imoments1[3780]/momentssd[2],imoments1[3834]/momentssd[3],imoments1[3875]/momentssd[4])
all1<-(c(kurtx=kurtx,skewx=skewx,momentsx,allrawmoBias,momentssd,medianmoments,standardizedm=standardizedm,allrawmo1,Huberx,SMWM9,imoments1,targetall))
SEbataches<-rbind(SEbataches,all1)
}
write.csv(SEbataches,paste("finite_Weibull_bootstrapsize_raw",batchnumber,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSE1_mean<-sqrt(colMeans((SEbataches[,11:786])^2))/sqrt(targetvar)
RMSE1_var<-sqrt(colMeans((SEbataches[,787:1339])^2))/simulatedbatch_asymptoticbias[60,3847]
RMSE1_tm<-sqrt(colMeans((SEbataches[,1340:1766])^2))/simulatedbatch_asymptoticbias[60,3848]
RMSE1_fm<-sqrt(colMeans((SEbataches[,1767:2067])^2))/simulatedbatch_asymptoticbias[60,3849]
RMSE1_skew<-sqrt(colMeans((SEbataches[,2068:3112])^2))
RMSE1_kurt<-sqrt(colMeans((SEbataches[,3113:3845])^2))
AB1_mean<-abs(colMeans((SEbataches[,11:786])))/sqrt(targetvar)
AB1_var<-abs(colMeans((SEbataches[,787:1339])))/simulatedbatch_asymptoticbias[60,3847]
AB1_tm<-abs(colMeans((SEbataches[,1340:1766])))/simulatedbatch_asymptoticbias[60,3848]
AB1_fm<-abs(colMeans((SEbataches[,1767:2067])))/simulatedbatch_asymptoticbias[60,3849]
AB1_skew<-abs(colMeans((SEbataches[,2068:3112])))
AB1_kurt<-abs(colMeans((SEbataches[,3113:3845])))
SEbatachesmean <- colMeans(SEbataches)
ratiomean1<-c(SEbatachesmean[3858:4633])/SEbatachesmean[4583]
meansd_unscaled1<-apply((SEbataches[1:batchsize,3858:4633]), 2, unbiasedsd)
mean_SE1<-meansd_unscaled1/sqrt(targetvar)
mean_SEbatachesmeanprocess<-t(t(SEbataches[1:batchsize,3858:4633])/ratiomean1)
meansd1<-apply((mean_SEbatachesmeanprocess), 2, unbiasedsd)
mean_SSE1<-meansd1/sqrt(targetvar)
ratiovar1<-SEbatachesmean[4634:5186]/SEbatachesmean[5156]
varsd_unscaled1<-apply((SEbataches[1:batchsize,4634:5186]), 2, unbiasedsd)
var_SE1<-varsd_unscaled1/simulatedbatch_asymptoticbias[60,3847]
var_SEbatachesvarprocess<-(t(t(SEbataches[1:batchsize,4634:5186])/ratiovar1))
varsd1<-apply(var_SEbatachesvarprocess, 2, unbiasedsd)
var_SSE1<-varsd1/simulatedbatch_asymptoticbias[60,3847]
ratiotm1<-SEbatachesmean[5187:5613]/SEbatachesmean[5589]
tmsd_unscaled1<-apply((SEbataches[1:batchsize,5187:5613]), 2, unbiasedsd)
tm_SE1<-tmsd_unscaled1/simulatedbatch_asymptoticbias[60,3848]
tm_SEbatachestmprocess<-(t(t(SEbataches[1:batchsize,5187:5613])/ratiotm1))
tmsd1<-apply(tm_SEbatachestmprocess, 2, unbiasedsd)
tm_SSE1<-tmsd1/simulatedbatch_asymptoticbias[60,3848]
ratiofm1<-SEbatachesmean[5614:5914]/SEbatachesmean[5896]
fmsd_unscaled1<-apply((SEbataches[1:batchsize,5614:5914]), 2, unbiasedsd)
fm_SE1<-fmsd_unscaled1/simulatedbatch_asymptoticbias[60,3849]
fm_SEbatachesfmprocess<-(t(t(SEbataches[1:batchsize,5614:5914])/ratiofm1))
fmsd1<-apply(fm_SEbatachesfmprocess, 2, unbiasedsd)
fm_SSE1<-fmsd1/simulatedbatch_asymptoticbias[60,3849]
ratio_skew1<-SEbatachesmean[5915:6959]/SEbatachesmean[6959]
skewsd_unscaled1<-apply((SEbataches[1:batchsize,5915:6959]), 2, unbiasedsd)
skew_SE1<-skewsd_unscaled1
skew_SEbatachesskewprocess<-(t(t(SEbataches[1:batchsize,5915:6959])/ratio_skew1))
skewsd1<-apply(skew_SEbatachesskewprocess, 2, unbiasedsd)
skew_SSE1<-skewsd1
ratio_kurt1<-SEbatachesmean[6960:7692]/SEbatachesmean[7692]
kurtsd_unscaled1<-apply((SEbataches[1:batchsize,6960:7692]), 2, unbiasedsd)
kurt_SE1<-kurtsd_unscaled1
kurt_SEbatacheskurtprocess<-(t(t(SEbataches[1:batchsize,6960:7692])/ratio_kurt1))
kurtsd1<-apply(kurt_SEbatacheskurtprocess, 2, unbiasedsd)
kurt_SSE1<-kurtsd1
allSE<-c(mean_SE1=mean_SE1,SEbatachesmean[1],var_SE1=var_SE1,SEbatachesmean[1],tm_SE1=tm_SE1,SEbatachesmean[1],fm_SE1=fm_SE1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSE_unstan<-c(SEbatachesmean[1],meansd_unscaled1=meansd_unscaled1,SEbatachesmean[1],varsd_unscaled1=varsd_unscaled1,SEbatachesmean[1],
tmsd_unscaled1=tmsd_unscaled1,SEbatachesmean[1],fmsd_unscaled1=fmsd_unscaled1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSSE<-c(SEbatachesmean[1],mean_SSE1=mean_SSE1,SEbatachesmean[1],var_SSE1=var_SSE1,SEbatachesmean[1],
tm_SSE1=tm_SSE1,SEbatachesmean[1],fm_SSE1=fm_SSE1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allSSE_unstand<-c(SEbatachesmean[1],meansd1=meansd1,SEbatachesmean[1],varsd1=varsd1,SEbatachesmean[1],
tmsd1=tmsd1,SEbatachesmean[1],fmsd1=fmsd1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allErrors<-c(samplesize=samplesize,kurt=SEbatachesmean[1],skew=SEbatachesmean[2],RMSE1_mean=RMSE1_mean,RMSE1_var=RMSE1_var,RMSE1_tm=RMSE1_tm,RMSE1_fm=RMSE1_fm,RMSE1_skew=RMSE1_skew,RMSE1_kurt=RMSE1_kurt,AB1_mean=AB1_mean,AB1_var=AB1_var,AB1_tm=AB1_tm,AB1_fm=AB1_fm,AB1_skew=AB1_skew,AB1_kurt=AB1_kurt,allSE=allSE,allSSE=allSSE,allSE_unstan=allSE_unstan,allSSE_unstand=allSSE_unstand,SEbatachesmean=SEbatachesmean)
allErrors
}
write.csv(simulatedbatch_bias_Monte,paste("finite_Weibull_bootstrapsize_raw",samplesize,".csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte_SE<-foreach(batchnumber =c((1:100)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
largesize<-round(batchnumber*13824*2/100)
a=allkurtWeibull[60]
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("finite_Weibull_bootstrapsize_raw",batchnumber,round(kurtx,digits = 1),".csv", sep = ","))
SEbatachesmean <- colMeans(SEbataches)
ratiomean1<-c(SEbatachesmean[3858:4633])/SEbatachesmean[4583]
meansd_unscaled1<-apply((SEbataches[1:batchsize,3858:4633]), 2, se_mean)
mean_SE1<-meansd_unscaled1/sqrt(targetvar)
mean_SEbatachesmeanprocess<-t(t(SEbataches[1:batchsize,3858:4633])/ratiomean1)
meansd1<-apply((mean_SEbatachesmeanprocess), 2, se_mean)
mean_SSE1<-meansd1/sqrt(targetvar)
ratiovar1<-SEbatachesmean[4634:5186]/SEbatachesmean[5156]
varsd_unscaled1<-apply((SEbataches[1:batchsize,4634:5186]), 2, se_mean)
var_SE1<-varsd_unscaled1/simulatedbatch_asymptoticbias[60,3847]
var_SEbatachesvarprocess<-(t(t(SEbataches[1:batchsize,4634:5186])/ratiovar1))
varsd1<-apply(var_SEbatachesvarprocess, 2, se_mean)
var_SSE1<-varsd1/simulatedbatch_asymptoticbias[60,3847]
ratiotm1<-SEbatachesmean[5187:5613]/SEbatachesmean[5589]
tmsd_unscaled1<-apply((SEbataches[1:batchsize,5187:5613]), 2, se_mean)
tm_SE1<-tmsd_unscaled1/simulatedbatch_asymptoticbias[60,3848]
tm_SEbatachestmprocess<-(t(t(SEbataches[1:batchsize,5187:5613])/ratiotm1))
tmsd1<-apply(tm_SEbatachestmprocess, 2, se_mean)
tm_SSE1<-tmsd1/simulatedbatch_asymptoticbias[60,3848]
ratiofm1<-SEbatachesmean[5614:5914]/SEbatachesmean[5896]
fmsd_unscaled1<-apply((SEbataches[1:batchsize,5614:5914]), 2, se_mean)
fm_SE1<-fmsd_unscaled1/simulatedbatch_asymptoticbias[60,3849]
fm_SEbatachesfmprocess<-(t(t(SEbataches[1:batchsize,5614:5914])/ratiofm1))
fmsd1<-apply(fm_SEbatachesfmprocess, 2, se_mean)
fm_SSE1<-fmsd1/simulatedbatch_asymptoticbias[60,3849]
ratio_skew1<-SEbatachesmean[5915:6959]/SEbatachesmean[6959]
skewsd_unscaled1<-apply((SEbataches[1:batchsize,5915:6959]), 2, se_mean)
skew_SE1<-skewsd_unscaled1
skew_SEbatachesskewprocess<-(t(t(SEbataches[1:batchsize,5915:6959])/ratio_skew1))
skewsd1<-apply(skew_SEbatachesskewprocess, 2, se_mean)
skew_SSE1<-skewsd1
ratio_kurt1<-SEbatachesmean[6960:7692]/SEbatachesmean[7692]
kurtsd_unscaled1<-apply((SEbataches[1:batchsize,6960:7692]), 2, se_mean)
kurt_SE1<-kurtsd_unscaled1
kurt_SEbatacheskurtprocess<-(t(t(SEbataches[1:batchsize,6960:7692])/ratio_kurt1))
kurtsd1<-apply(kurt_SEbatacheskurtprocess, 2, se_mean)
kurt_SSE1<-kurtsd1
allSE<-c(mean_SE1=mean_SE1,SEbatachesmean[1],var_SE1=var_SE1,SEbatachesmean[1],tm_SE1=tm_SE1,SEbatachesmean[1],fm_SE1=fm_SE1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSE_unstan<-c(SEbatachesmean[1],meansd_unscaled1=meansd_unscaled1,SEbatachesmean[1],varsd_unscaled1=varsd_unscaled1,SEbatachesmean[1],
tmsd_unscaled1=tmsd_unscaled1,SEbatachesmean[1],fmsd_unscaled1=fmsd_unscaled1,SEbatachesmean[1],skew_SE1=skew_SE1,SEbatachesmean[1],kurt_SE1=kurt_SE1
)
allSSE<-c(SEbatachesmean[1],mean_SSE1=mean_SSE1,SEbatachesmean[1],var_SSE1=var_SSE1,SEbatachesmean[1],
tm_SSE1=tm_SSE1,SEbatachesmean[1],fm_SSE1=fm_SSE1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
allSSE_unstand<-c(SEbatachesmean[1],meansd1=meansd1,SEbatachesmean[1],varsd1=varsd1,SEbatachesmean[1],
tmsd1=tmsd1,SEbatachesmean[1],fmsd1=fmsd1,SEbatachesmean[1],skew_SSE1=skew_SSE1,SEbatachesmean[1],kurt_SSE1=kurt_SSE1
)
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
allErrors<-c(samplesize=samplesize,kurt=SEbatachesmean[1],skew=SEbatachesmean[2],se_mean=se_mean_all1,allSE=allSE,allSSE=allSSE,allSE_unstan=allSE_unstan,allSSE_unstand=allSSE_unstand,SEbatachesmean=SEbatachesmean)
allErrors
}
write.csv(simulatedbatch_bias_Monte_SE,paste("finite_Weibull_bootstrapsize_raw_error",samplesize,".csv", sep = ","), row.names = FALSE)
kurtgamma<- read.csv(("kurtgamma_31100.csv"))
allkurtgamma<-unlist(kurtgamma)
simulatedbatch_asymptoticbias<-foreach(batchnumber = (1:length(allkurtgamma)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(randtoolbox)
library(NRSReview)
setSeed(1)
set.seed(1)
a=allkurtgamma[batchnumber]
x<-c(dsgamma(uni=quasiuni_asymptotic, shape=a/1, rate = 1))
targetm<-a
targetvar<-(a)
targettm<-((sqrt(a))^3)*2/sqrt(a)
targetfm<-((sqrt(a))^4)*((6/(a))+3)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx, tol = 1e-10)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted=TRUE)
imoments1<-imoments(x=sortedx,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 5,releaseall=TRUE,standist_d=d_values,standist_I=I_values,standist_Ismoments=Ismoments_values,standist_Imoments=Imoments_values,orderlist1_sorted20=orderlist1_AB2_asymptotic,orderlist1_sorted30=orderlist1_AB3_asymptotic,orderlist1_sorted40=orderlist1_AB4_asymptotic,orderlist1_hlsmall=orderlist1_hllarge_asymptotic,orderlist1_hllarge=orderlist1_hllarge_asymptotic,percentage=1/24,batch="auto",stepsize=1000,criterion=1e-10,boot=TRUE)
imoments1<-unlist(imoments1)
momentsx<-standardizedmoments(x=sortedx,releaseall = TRUE)
#D Olive, Robust estimators for transformed location scale families. Unpubl. manuscript 1025 available from (www. math. siu. edu/olive/preprints. htm) (2006).
medianMAD1<-Weibull_median_MAD_estimator(sortedx)
#NB Marks, Estimation of weibull parameters from common percentiles. J. applied Stat. 32, 17–24 (2005).
QE1<-Weibull_quantile_estimator(x=sortedx,sorted=TRUE)
alpha1<-QE1[1]-0.3
alpha2<-QE1[1]+0.3
#X He, WK Fung, Method of medians for lifetime data with weibull models. Stat. medicine 18, 1993–2009 (1999)
RMLE1<-Weibull_RMLE(sortedx,alpha1=alpha1,alpha2=alpha2)
#all parameter setting are from
#K Boudt, D Caliskan, C Croux, Robust explicit estimators of weibull parameters. Metrika 73, 187–209 (2011).
moments_medianMAD1<-Weibull_moments(alpha=medianMAD1[1],lambda=medianMAD1[2])
moments_QE1<-Weibull_moments(alpha=QE1[1],lambda=QE1[2])
moments_RMLE1<-Weibull_moments(alpha=RMLE1[1],lambda=RMLE1[2])
MoM2<-median_of_means(sortedx,korder=2)
MoM3<-median_of_means(sortedx,korder=3)
MoM4<-median_of_means(sortedx,korder=4)
MoM5<-median_of_means(sortedx,korder=5)
MoM6<-median_of_means(sortedx,korder=6)
MoRMall<-mHLM_all(x=sortedx,max_dim=6,orderlists=orderlist1_hllarge_asymptotic_rand,boot=TRUE,quasi=FALSE,largesize=largesize)
MoRMall<-unlist(MoRMall)
sortedx<-c()
momentssd<-c(sd=sqrt(momentsx[2]),imoments1[3899],imoments1[3900],imoments1[3901])
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)-targetm)/sqrt(targetvar),
secondbias=abs(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])-targetvar)/momentssd[2],
thirdbias=abs(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])-targettm)/momentssd[3],
fourbias=abs(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])-targetfm)/momentssd[4],
skewbias=abs(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])-skewx),
kurtbias=abs(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902])-kurtx)
)
allrawmo1<-c(first=(c(Huberx,SMWM9,imoments1[1],momentsx[1],imoments1[(1779):(2498)],imoments1[3699:3736],mean_medianMAD1=moments_medianMAD1[1],mean_QE1=moments_QE1[1],mean_RMLE1=moments_RMLE1[1],MoM2=MoM2,MoM3=MoM3,MoM4=MoM4,MoM5=MoM5,MoM6=MoM6,MoRMall=MoRMall)),
second=(c(imoments1[2],momentsx[2],imoments1[2499:3018],imoments1[3773:3800],var_medianMAD1=moments_medianMAD1[2],var_QE1=moments_QE1[2],var_RMLE1=moments_RMLE1[2])),
third=(c(imoments1[3],momentsx[3],imoments1[3019:3418],imoments1[3827:3848],tm_medianMAD1=moments_medianMAD1[3],tm_QE1=moments_QE1[3],tm_RMLE1=moments_RMLE1[3])),
fourth=(c(imoments1[4],momentsx[4],imoments1[3419:3698],imoments1[3869:3884],fm_medianMAD1=moments_medianMAD1[4],fm_QE1=moments_QE1[4],fm_RMLE1=moments_RMLE1[4])),
skew=(c(imoments1[5],momentsx[7],imoments1[737:1778],imoments1[3903])),
kurt=(c(imoments1[6],momentsx[8],imoments1[7:736],imoments1[3902]))
)
medianmoments<-c(imoments1[3706],imoments1[3780],imoments1[3834],imoments1[3875])
standardizedm<-c(imoments1[3706]/sqrt(targetvar),imoments1[3780]/momentssd[2],imoments1[3834]/momentssd[3],imoments1[3875]/momentssd[4])
all1<-(c(kurtx=kurtx,skewx=skewx,momentsx,allrawmoBias,momentssd,medianmoments,standardizedm=standardizedm,allrawmo1,Huberx,SMWM9,imoments1,targetall))
}
write.csv(simulatedbatch_asymptoticbias,paste("asymptotic_gamma_raw_Process",largesize,".csv", sep = ","), row.names = FALSE)