A High-Dimensional Cramér–von Mises Test

Danna Zhang and Mengyu Xu ()
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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

Mathematics, 2024, vol. 12, issue 22, 1-23

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.

Keywords: Cramér–von Mises statistic; goodness-of-fit test; high-dimensional data; resampling; linear combination of chi-squared distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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