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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.
    2. 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.
    3. Arup Bose & Probal Chaudhuri, 1993. "On the dispersion of multivariate median," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 541-550, September.
    4. Lan Wang & Bo Peng & Runze Li, 2015. "A High-Dimensional Nonparametric Multivariate Test for Mean Vector," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1658-1669, December.
    5. 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.
    6. Guanghui Cheng & Baisen Liu & Liuhua Peng & Baoxue Zhang & Shurong Zheng, 2019. "Testing the equality of two high‐dimensional spatial sign covariance matrices," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 257-271, March.
    7. Jin Wang & Weihua Zhou, 2015. "Effect of kurtosis on efficiency of some multivariate medians," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 331-348, September.
    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.
    9. Srivastava, Muni S. & Katayama, Shota & Kano, Yutaka, 2013. "A two sample test in high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 349-358.
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