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3_Asymptotic_NRSs_RMSEcalibration.R
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3_Asymptotic_NRSs_RMSEcalibration.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
#bootsize for bootstrap approximation of the distributions of the kernal of U-statistics.
n <- 331776*3*8
(n%%10)==0
# maximum order of moments
morder <- 4
#large sample size (approximating asymptotic)
largesize<-331776*8
#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...
#load asymptotic d for two parameter distributions
#set the stop criterion
criterionset=1e-10
samplesize=331776*8
batchsizebase=100
orderlist1_AB2<-createorderlist(quni1=quasiuni_sorted2,size=largesize,interval=8,dimension=2)
orderlist1_AB2<-orderlist1_AB2[1:largesize,]
orderlist1_AB3<-createorderlist(quni1=quasiuni_sorted3,size=largesize,interval=8,dimension=3)
orderlist1_AB3<-orderlist1_AB3[1:largesize,]
orderlist1_AB4<-createorderlist(quni1=quasiuni_sorted4,size=largesize,interval=8,dimension=4)
orderlist1_AB4<-orderlist1_AB4[1:largesize,]
batchsize=batchsizebase
n <- samplesize
setSeed(1)
unibatchran<-matrix(SFMT(samplesize*batchsize),ncol=batchsize)
unibatch<-colSort(unibatchran, descend = FALSE, stable = FALSE, parallel = TRUE)
#input the d value table previously generated
d_values<- read.csv(("d_values.csv"))
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<-createorderlist(quni1=quasiuni_M[,1:6],size=largesize,interval=8,dimension=6)
orderlist1_hllarge<-orderlist1_hllarge[1:largesize,]
#Then, start the Monte Simulation
kurtlognorm<- read.csv(("kurtlognorm_31180.csv"))
allkurtlognorm<-unlist(kurtlognorm)
simulatedbatch_bias_Monte<-foreach(batchnumber =c((1:length(allkurtlognorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
set.seed(1)
a=allkurtlognorm[batchnumber]
targetm<-exp((a^2)/2)
targetvar<-(exp((a/1)^2)*(-1+exp((a/1)^2)))
targettm<-sqrt(exp((a/1)^2)-1)*((2+exp((a/1)^2)))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^3)
targetfm<-((-3+exp(4*((a/1)^2))+2*exp(3*((a/1)^2))+3*exp(2*((a/1)^2))))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^4)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
RMSEbataches<-c()
for (batch1 in c(1:batchsize)){
x<-c(dslnorm(uni=unibatch[,batch1], meanlog =0, sdlog = a/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()
rqmoments1<-rqmoments(x=sortedx,start_kurt=kurtx,start_skew=skewx,dtype1=1,releaseall=TRUE,standist_d=d_values,orderlist1_sorted20=orderlist1_AB2,orderlist1_sorted30=orderlist1_AB3,orderlist1_sorted40=orderlist1_AB4,orderlist1_hlsmall=orderlist1_hllarge,orderlist1_hllarge=orderlist1_hllarge,percentage=1/24,batch="auto",stepsize=1000,criterion=criterionset)
standardizedmomentsx<-standardizedmoments(x=sortedx)
sortedx<-c()
all1<-unlist(c(rqmoments1,targetall,standardizedmomentsx))
RMSEbataches<-rbind(RMSEbataches,all1)
}
write.csv(RMSEbataches,paste("asymptotic_lognorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSEbataches <- apply(RMSEbataches[1:batchsize,], 2, as.numeric)
RMSEbatachesmean <-apply(RMSEbataches, 2, calculate_column_mean)
rqkurt<-sqrt(colMeans((RMSEbataches[1:batchsize,c(1:728,1961:2688)]-kurtx)^2))
rqskew<-sqrt(colMeans((RMSEbataches[1:batchsize,c(729:1768,2689:3728)]-skewx)^2))
rankkurtall1<-rank(rqkurt)
rankskewall1<-rank(rqskew)
allresultsRMSE<-c(samplesize=samplesize,type=4,kurtx=kurtx,skewx=skewx,rankkurtall1,rankskewall1,RMSEbatachesmean,RMSErqkurt=rqkurt,RMSErqskew=rqskew)
}
write.csv(simulatedbatch_bias_Monte,paste("asymptotic_lognorm_Icalibration_raw",largesize,".csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte<- read.csv(paste("asymptotic_lognorm_Icalibration_raw",largesize,".csv", sep = ","))
Optimum_RMSE<-simulatedbatch_bias_Monte[,1:3540]
write.csv(Optimum_RMSE,paste("asymptotic_I_lognorm.csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte_SE<-foreach(batchnumber =c((1:length(allkurtlognorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
a=allkurtlognorm[batchnumber]
targetm<-exp((a^2)/2)
targetvar<-(exp((a/1)^2)*(-1+exp((a/1)^2)))
targettm<-sqrt(exp((a/1)^2)-1)*((2+exp((a/1)^2)))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^3)
targetfm<-((-3+exp(4*((a/1)^2))+2*exp(3*((a/1)^2))+3*exp(2*((a/1)^2))))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^4)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("asymptotic_lognorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
rqkurt_se<-apply(((SEbataches[1:batchsize,c(1:728,1961:2688)])), 2, se_sd)
rqskew_se<-apply((SEbataches[1:batchsize,c(729:1768,2689:3728)]), 2, se_sd)
allresultsSE<-c(samplesize=samplesize,type=4,kurtx,skewx,se_mean_all1,rqkurt_se,rqskew_se)
allresultsSE
}
write.csv(simulatedbatch_bias_Monte_SE,paste("asymptotic_lognorm_Icalibration_raw_error",largesize,".csv", sep = ","), row.names = FALSE)
asymptotic_I_lognorm<- read.csv(("asymptotic_I_lognorm.csv"))
kurtgnorm<- read.csv(("kurtgnorm_21180.csv"))
allkurtgnorm<-unlist(kurtgnorm)
simulatedbatch_bias_Monte<-foreach(batchnumber =c((1:length(allkurtgnorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
set.seed(1)
a=allkurtgnorm[batchnumber]
targetm<-0
targetvar<-gamma(3/a)/((gamma(1/a)))
targettm<-0
targetfm<-((gamma(3/a)/((gamma(1/a))))^2)*gamma(5/a)*gamma(1/a)/((gamma(3/a))^2)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
RMSEbataches<-c()
for (batch1 in c(1:batchsize)){
x<-c(dsgnorm(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()
rqmoments1<-rqmoments(x=sortedx,start_kurt=kurtx,start_skew=skewx,dtype1=1,releaseall=TRUE,standist_d=d_values,orderlist1_sorted20=orderlist1_AB2,orderlist1_sorted30=orderlist1_AB3,orderlist1_sorted40=orderlist1_AB4,orderlist1_hlsmall=orderlist1_hllarge,orderlist1_hllarge=orderlist1_hllarge,percentage=1/24,batch="auto",stepsize=1000,criterion=criterionset)
standardizedmomentsx<-standardizedmoments(x=sortedx)
sortedx<-c()
all1<-unlist(c(rqmoments1,targetall,standardizedmomentsx))
RMSEbataches<-rbind(RMSEbataches,all1)
}
write.csv(RMSEbataches,paste("asymptotic_gnorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSEbataches <- apply(RMSEbataches[1:batchsize,], 2, as.numeric)
RMSEbatachesmean <-apply(RMSEbataches, 2, calculate_column_mean)
rqkurt<-sqrt(colMeans((RMSEbataches[1:batchsize,c(1:728,1961:2688)]-kurtx)^2))
rqskew<-sqrt(colMeans((RMSEbataches[1:batchsize,c(729:1768,2689:3728)]-skewx)^2))
rankkurtall1<-rank(rqkurt)
rankskewall1<-rank(rqskew)
allresultsRMSE<-c(samplesize=samplesize,type=5,kurtx=kurtx,skewx=skewx,rankkurtall1,rankskewall1,RMSEbatachesmean,RMSErqkurt=rqkurt,RMSErqskew=rqskew)
}
write.csv(simulatedbatch_bias_Monte,paste("asymptotic_gnorm_Icalibration_raw",largesize,".csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte<- read.csv(paste("asymptotic_gnorm_Icalibration_raw",largesize,".csv", sep = ","))
Optimum_RMSE<-simulatedbatch_bias_Monte[,1:3540]
write.csv(Optimum_RMSE,paste("asymptotic_I_gnorm.csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte_SE<-foreach(batchnumber =c((1:length(allkurtgnorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(NRSReview)
a=allkurtgnorm[batchnumber]
ttargetm<-0
targetvar<-gamma(3/a)/((gamma(1/a)))
targettm<-0
targetfm<-((gamma(3/a)/((gamma(1/a))))^2)*gamma(5/a)*gamma(1/a)/((gamma(3/a))^2)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("asymptotic_gnorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
rqkurt_se<-apply(((SEbataches[1:batchsize,c(1:728,1961:2688)])), 2, se_sd)
rqskew_se<-apply((SEbataches[1:batchsize,c(729:1768,2689:3728)]), 2, se_sd)
allresultsSE<-c(samplesize=samplesize,type=5,kurtx,skewx,se_mean_all1,rqkurt_se,rqskew_se)
allresultsSE
}
write.csv(simulatedbatch_bias_Monte_SE,paste("asymptotic_gnorm_Icalibration_raw_error",largesize,".csv", sep = ","), row.names = FALSE)
asymptotic_I_gnorm<- read.csv(("asymptotic_I_gnorm.csv"))
asymptotic_I_lognorm<- read.csv(("asymptotic_I_lognorm.csv"))
names(asymptotic_I_lognorm)<-1:ncol(asymptotic_I_lognorm)
names(asymptotic_I_gnorm)<-1:ncol(asymptotic_I_lognorm)
asymptotic_I_lognorm<-rbind(asymptotic_I_lognorm,asymptotic_I_gnorm)
asymptotic_I_gnorm<- read.csv(("asymptotic_I_lognorm.csv"))
names(asymptotic_I_lognorm)<-names(asymptotic_I_gnorm)
write.csv(asymptotic_I_lognorm,paste("asymptotic_I.csv", sep = ","), row.names = FALSE)
stopCluster(cl)
registerDoSEQ()