Asymptotics and practical aspects of testing normality with kernel methods

Natsumi Makigusa; Kanta Naito

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arXiv · 1902.03241

Asymptotics and practical aspects of testing normality with kernel methods

Natsumi Makigusa·Kanta Naito

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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.

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BibTeX RIS

Natsumi Makigusa, Kanta Naito. 2019-02-08. Asymptotics and practical aspects of testing normality with kernel methods. https://arxiv.org/abs/1902.03241

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