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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.06134 |
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| _version_ | 1866908581728616448 |
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| author | Cabaña, A. Cabaña, E. M. |
| author_facet | Cabaña, A. Cabaña, E. M. |
| contents | A construction of $p$-parameter Brownian sheet on the hypercube $C=[0,1]^p$ as a sum of $2^p$ independent Gaussian processes is obtained. The terms are closely related to Brownian pillows, and the probability laws of their $L^2(C)$ squared norms are computed.
This allows us to propose consistent tests of uniformity for samples of i.i.d. random vectors on $C$. A comparison of powers of the new tests with those of several uniformity tests found in the statistical literature completes the article. The proposed tests show a good performance in detecting copula alternatives.
Keywords: Brownian sheet, multivariate uniformity tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brownian sheet and uniformity tests on the hypercube Cabaña, A. Cabaña, E. M. Statistics Theory A construction of $p$-parameter Brownian sheet on the hypercube $C=[0,1]^p$ as a sum of $2^p$ independent Gaussian processes is obtained. The terms are closely related to Brownian pillows, and the probability laws of their $L^2(C)$ squared norms are computed. This allows us to propose consistent tests of uniformity for samples of i.i.d. random vectors on $C$. A comparison of powers of the new tests with those of several uniformity tests found in the statistical literature completes the article. The proposed tests show a good performance in detecting copula alternatives. Keywords: Brownian sheet, multivariate uniformity tests. |
| title | Brownian sheet and uniformity tests on the hypercube |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2509.06134 |