 Asymptotics and practical aspects of testing normality with kernel methodsNatsumi Makigusa and Kanta Naito Journal of Multivariate Analysis, 2020, vol. 180, issue C 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. Keywords: Asymptotics; Hilbert space; Kernel method; Testing normality (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x20302463 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2020.104665 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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