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

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  • Li, Weiming
  • Xu, Yangchang

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.

Suggested Citation

  • Li, Weiming & Xu, Yangchang, 2022. "Asymptotic properties of high-dimensional spatial median in elliptical distributions with application," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000197
    DOI: 10.1016/j.jmva.2022.104975
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    References listed on IDEAS

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    1. Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
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    8. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
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