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Tests of elliptical symmetry and the asymptotic tail behavior of the statistics

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Abstract

In this paper, some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.

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Authors and Affiliations

  1. Department of Science and Art, China University of Mining and Technology, 100083, Beijing

    Jing Ping & Zhu Lixing

  2. Probability Lab, Institute of Applied Mathematics, The Chinese Academy of Sciences, 100080, Beijing

    Jing Ping & Zhu Lixing

Authors
  1. Jing Ping
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  2. Zhu Lixing
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Project Supported by the NSF of China and the state Education Commission for Returnhed Scholar.

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Ping, J., Lixing, Z. Tests of elliptical symmetry and the asymptotic tail behavior of the statistics. Appl. Math. Chin. Univ. 14, 423–432 (1999). https://doi.org/10.1007/s11766-999-0072-4

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  • DOI: https://doi.org/10.1007/s11766-999-0072-4

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