The goal of KEPTED is to provide an implementation of a kernel-embedding of probability test for elliptical distribution, which has been derived by Tang and Li (2024). This is an asymptotic test for elliptical distribution under general alternatives, and the location and shape parameters are assumed to be unknown. Some side-products are posted, including the transformation between rectangular and polar coordinates and two product-type kernel functions.

You can install the development version of KEPTED from GitHub with:

# install.packages("devtools")
devtools::install_github("tyy20/KEPTED")

This is a basic example which shows you how to solve a common problem:

library(KEPTED)

n=200
d=3

## test under a null distribution
X=matrix(rnorm(d*n),nrow=n,ncol=d)
EllKEPT(X,kerU="Gaussian",kerTheta="Gaussian")
EllKEPT(X,kerU="PIQ",kerTheta="PIQ")

## test under an alternative distribution
X=matrix(rchisq(d*n,2),nrow=n,ncol=d)
EllKEPT(X,kerU="Gaussian",kerTheta="Gaussian")
EllKEPT(X,kerU="PIQ",kerTheta="PIQ")

Tang, Y. and Li, B. (2024), “A nonparametric test for elliptical distribution based on kernel embedding of probabilities” (https://arxiv.org/abs/2306.10594)