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Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory

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Abstract

This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size. The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations. Further, some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity. Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610064, China

    Shou-cheng Yuan & Jie Zhou

  2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    Jian-xin Pan

  3. School of Computer and Data Engineering, Zhejiang University Ningbo Institute of Technology, Ningbo, 315100, China

    Jie-qiong Shen

Authors
  1. Shou-cheng Yuan
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  2. Jie Zhou
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  3. Jian-xin Pan
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  4. Jie-qiong Shen
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Corresponding author

Correspondence to Jie Zhou.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 61374027, 11871357) and by the Sichuan Science and Technology Program (Nos. 2019YJ0122).

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Yuan, Sc., Zhou, J., Pan, Jx. et al. Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory. Acta Math. Appl. Sin. Engl. Ser. 37, 214–231 (2021). https://doi.org/10.1007/s10255-021-1004-1

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  • DOI: https://doi.org/10.1007/s10255-021-1004-1

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