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A High-Dimensional Cramér–von Mises Test

Author

Listed:
  • Danna Zhang

    (Department of Mathematics, University of California San Diego, San Diego, CA 92093, USA)

  • Mengyu Xu

    (Department of Statistics and Data Science, University of Central Florida, Orlando, FL 32816, USA)

Abstract

The Cramér–von Mises test provides a useful criterion for assessing goodness of fit in various problems. In this paper, we introduce a novel Cramér–von Mises-type test for testing distributions of high-dimensional continuous data. We establish an asymptotic theory for the proposed test statistics based on quadratic functions in high-dimensional stochastic processes. To estimate the limiting distribution of the test statistic, we propose two practical approaches: a plug-in calibration method and a subsampling method. Theoretical justifications are provided for both techniques. Numerical simulation also confirms the convergence of the proposed methods.

Suggested Citation

  • Danna Zhang & Mengyu Xu, 2024. "A High-Dimensional Cramér–von Mises Test," Mathematics, MDPI, vol. 12(22), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3467-:d:1515447
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    References listed on IDEAS

    as
    1. Gary M. Koop, 2013. "Forecasting with Medium and Large Bayesian VARS," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 177-203, March.
    2. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    3. Jiajuan Liang & Man-Lai Tang & Xuejing Zhao, 2019. "Testing high-dimensional normality based on classical skewness and Kurtosis with a possible small sample size," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(23), pages 5719-5732, December.
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