Asymptotics and practical aspects of testing normality with kernel methods
Abstract
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the test under a fixed alternative hypothesis is developed, which implies that the test has consistency. Asymptotic distribution of the test under a sequence of local alternatives is also derived, from which asymptotic null distribution of the test is obtained. A concrete expression for the integral kernel associated with the null distribution is derived under the use of the Gaussian kernel, allowing the implementation of a reliable approximation of the null distribution. Simulations and applications to real data sets are reported with emphasis on high-dimension low-sample size cases.
Cite
@article{arxiv.1902.03241,
title = {Asymptotics and practical aspects of testing normality with kernel methods},
author = {Natsumi Makigusa and Kanta Naito},
journal= {arXiv preprint arXiv:1902.03241},
year = {2019}
}