Asymptotic properties of high-dimensional spatial median in elliptical distributions with application

Weiming Li and Yangchang Xu

Journal of Multivariate Analysis, 2022, vol. 190, issue C

Abstract: This paper is concerned with asymptotic behaviors of sample spatial medians under elliptical distributions in a high-dimensional asymptotic framework, where the dimension of observations diverges to infinity at the same rate as the sample size. The first and second order asymptotic limits of the Euclidean distance between the sample spatial median and its population counterpart are established under such an asymptotic regime. Based on these findings, new one-sample and two-sample test procedures for high-dimensional mean vectors are developed.

Keywords: Elliptical distribution; High-dimensional data; Mean test; Spatial median (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2022.104975

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