In GerritEichner/kader: Kernel Adaptive Density Estimation and Regression

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kader

The goal of kader is to supply functions to compute nonparametric kernel estimators for

density estimation using a data-adjusted kernel or an appropriate rank-transformation, and for
regression using a data-adjusted kernel.

The functions are based on the theory introduced in

Srihera, R., Stute, W. (2011): Kernel adjusted density estimation. Statistics and Probability Letters 81, 571 - 579, URL http://dx.doi.org/10.1016/j.spl.2011.01.013.
Eichner, G., Stute, W. (2012): Kernel adjusted nonparametric regression. Journal of Statistical Planning and Inference 142, 2537 - 2544, URL http://dx.doi.org/10.1016/j.jspi.2012.03.011.
Eichner, G., Stute, W. (2013): Rank Transformations in Kernel Density Estimation. Journal of Nonparametric Statistics 25(2), 427 - 445, URL http://dx.doi.org/10.1080/10485252.2012.760737.

A very brief summary of the theory and sort of a vignette is presented in Eichner, G. (2017): Kader - An R package for nonparametric kernel adjusted density estimation and regression. In: Ferger, D., et al. (eds.): From Statistics to Mathematical Finance, Festschrift in Honour of Winfried Stute. Springer International Publishing. To appear in Jan. 2018. DOI then(!) presumably: 10.1007/978-3-319-50986-0.

Installation

You can install kader from CRAN with:

install.packages("kader")

or from github with:

# install.packages("devtools")
devtools::install_github("GerritEichner/kader")

Example

This example shows you how to estimate at $x_0 = 2$ the value of the density function of the probability distribution underlying Old-Faithful's eruptions data using the (nonrobust) method of Srihera & Stute (2011). The initial grid (given to Sigma) on which the minimization of the estimated MSE as a function of a (kernel-adjusting) scale parameter $\sigma$ is started is rather coarse here to save computing time.

library(kader)
x0 <- 2
sigma <- seq(0.01, 10, length = 21)
fit <- kade(x = x0, data = faithful$eruptions, method = "nonrobust",
  Sigma = sigma, ticker = TRUE)
print(fit)