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Asymptotics and practical aspects of testing normality with kernel methods

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  • Makigusa, Natsumi
  • Naito, Kanta

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.

Suggested Citation

  • Makigusa, Natsumi & Naito, Kanta, 2020. "Asymptotics and practical aspects of testing normality with kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x20302463
    DOI: 10.1016/j.jmva.2020.104665
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    References listed on IDEAS

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    4. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    5. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
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