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The KDE object in this project allows you to estimate the distribution of numerical data with user-defined granularity by introducing the free parameter cuts. This parameter allows for control over the order of estimation.
The methodology for construction is outlined in the notebook kde.ipynb and the neccessary code for computation is given in KernelDensityEstimator.py.
Current KDE options include:
- Gaussian (defualt, and most robust estimator)
- Cauchy
- Poisson (not very useful but has its uses; can be used for skew-left-decreasing data on the interval
[0,N])
If estimating using Gaussian, I recommend using something like Sturgis' Rule (cuts = 1 + 3.3*log10(n), where n = len(data)) for determining the number of cuts to use. Obviously, increasing the number of cuts too high will result in a gross overfitting of the estimation.
If estimating using Cauchy, I find that increasing the number of cuts by around a factor of 2 helps the appearance of the estimation. Using something like Rice's Rule (cuts = 2n^(1/3), where n = len(data)) is beneficial here.
If estimating using Poisson, ensure that 1) The support is [0,N] for some large integer N, 2) The data is roughly monotone decreasing. If it can be helped, try to additionally use integer valued data (this is not neccessary however).