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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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    5. Li, Yang & Wang, Zhaojun & Zou, Changliang, 2016. "A simpler spatial-sign-based two-sample test for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 192-198.
    6. Changliang Zou & Liuhua Peng & Long Feng & Zhaojun Wang, 2014. "Multivariate sign-based high-dimensional tests for sphericity," Biometrika, Biometrika Trust, vol. 101(1), pages 229-236.
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