Eigenvalues approximation of integral covariance operators with applications to weighted $L^2$ statistics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913468689416192 |
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| author | Ebner, Bruno Jiménez-Gamero, María Dolores Milošević, Bojana |
| author_facet | Ebner, Bruno Jiménez-Gamero, María Dolores Milošević, Bojana |
| contents | Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In statistics this problem arises for instance in the asymptotic null distribution of goodness-of-fit test statistics of weighted $L^2$-type. For this problem we present the Rayleigh-Ritz method to approximate the eigenvalues. The usefulness of these approximations is shown by high lightening implications such as critical value approximation and theoretical comparison of test statistics by means of Bahadur efficiencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalues approximation of integral covariance operators with applications to weighted $L^2$ statistics Ebner, Bruno Jiménez-Gamero, María Dolores Milošević, Bojana Statistics Theory Numerical Analysis 62E20, 62E17 Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In statistics this problem arises for instance in the asymptotic null distribution of goodness-of-fit test statistics of weighted $L^2$-type. For this problem we present the Rayleigh-Ritz method to approximate the eigenvalues. The usefulness of these approximations is shown by high lightening implications such as critical value approximation and theoretical comparison of test statistics by means of Bahadur efficiencies. |
| title | Eigenvalues approximation of integral covariance operators with applications to weighted $L^2$ statistics |
| topic | Statistics Theory Numerical Analysis 62E20, 62E17 |
| url | https://arxiv.org/abs/2408.08064 |