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On Estimated Projection Pursuit-Type Crámer-von Mises Statistics,

Author

Listed:
  • Zhu, Li-Xing
  • Fang, Kai-Tai
  • Bhatti, M Ishaq

Abstract

This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Crámer-Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered.

Suggested Citation

  • Zhu, Li-Xing & Fang, Kai-Tai & Bhatti, M Ishaq, 1997. "On Estimated Projection Pursuit-Type Crámer-von Mises Statistics, ," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 1-14, October.
    • Handle: RePEc:eee:jmvana:v:63:y:1997:i:1:p:1-14
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    Cited by:

    1. Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    2. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    3. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
    4. Xu, Kai & Zhou, Yeqing, 2021. "Projection-averaging-based cumulative covariance and its use in goodness-of-fit testing for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).

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