Minimax Estimation Problem for Periodically Correlated Stochastic Processes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912673447280640 |
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| author | Dubovets'ka, Iryna Moklyachuk, Mykhailo |
| author_facet | Dubovets'ka, Iryna Moklyachuk, Mykhailo |
| contents | The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functionals are proposed in the case where spectral densities are exactly known and in the case where the spectral densities are unknown while a class of admissible spectral densities is given. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed for a given class of admissible spectral densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimax Estimation Problem for Periodically Correlated Stochastic Processes Dubovets'ka, Iryna Moklyachuk, Mykhailo Statistics Theory 60G25, 62M20, 93E10 The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functionals are proposed in the case where spectral densities are exactly known and in the case where the spectral densities are unknown while a class of admissible spectral densities is given. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed for a given class of admissible spectral densities. |
| title | Minimax Estimation Problem for Periodically Correlated Stochastic Processes |
| topic | Statistics Theory 60G25, 62M20, 93E10 |
| url | https://arxiv.org/abs/2510.14033 |