A High-Dimensional Cramér–von Mises Test
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 ba...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/22/3467 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |