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High-dimensional rank tests for sphericity

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  • Feng, Long
  • Liu, Binghui

Abstract

In recent years, procedures for testing distributional sphericity have attracted increased attention, especially in high-dimensional settings. A prominent problem in this context is the development of robust and efficient test statistics. In this paper, we propose two novel rank tests inspired by Spearman’s rho and Kendall’s tau for high-dimensional problems. Due to the “blessing of dimension”, estimation of masses of nuisance parameters is avoided, which allows our procedures to work in arbitrary large dimension. The asymptotic normality of the proposed tests is established for elliptical distributions and their performance is investigated over a wide range of simulation set-ups.

Suggested Citation

  • Feng, Long & Liu, Binghui, 2017. "High-dimensional rank tests for sphericity," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 217-233.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:217-233
    DOI: 10.1016/j.jmva.2017.01.003
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    References listed on IDEAS

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    1. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    2. 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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    Cited by:

    1. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "Multivariate tests of independence and their application in correlation analysis between financial markets," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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