Kernel Estimators for the Mean Function of a Stochastic Process under Sparse Design Conditions Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2022, Volume: 32, Number: 4, Pages: 269-276 Pages count : 8 DOI: 10.1134/S1055134422040034 | ||
| Tags | kernel estimator; mean function estimation; nonparametric regression; sparse fixed design; sparse random design; strongly dependent design elements; uniform consistency | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-21-00414 |
Abstract:
The problem of nonparametric estimation of the mean function for a continuous random process is considered, when the noisy values of each of its independent trajectories are observed in some random time points — design elements. Under broad conditions on the dependence of design elements, uniformly consistent estimates are constructed for the mean function in the case of one of the versions of so-called sparse design, when the number of design elements for each of the trajectories is the same and independent of the growing number of series of observations. Unlike the papers of predecessors, we do not require that the set of design elements consist of independent identically distributed or weakly dependent random variables. Regarding the design, it is only assumed that the entire set of design points with a high probability forms a refining partition of the domain of the random process under consideration.
Cite:
Linke Y.Y.
Kernel Estimators for the Mean Function of a Stochastic Process under Sparse Design Conditions
Siberian Advances in Mathematics. 2022. V.32. N4. P.269-276. DOI: 10.1134/S1055134422040034 Scopus РИНЦ OpenAlex
Kernel Estimators for the Mean Function of a Stochastic Process under Sparse Design Conditions
Siberian Advances in Mathematics. 2022. V.32. N4. P.269-276. DOI: 10.1134/S1055134422040034 Scopus РИНЦ OpenAlex
Original:
Линке Ю.Ю.
Ядерные оценки для функции математического ожидания случайного процесса в условиях разреженного дизайна
Математические труды. 2022. Т.25. №2. С.149-161. DOI: 10.33048/mattrudy.2022.25.206 РИНЦ
Ядерные оценки для функции математического ожидания случайного процесса в условиях разреженного дизайна
Математические труды. 2022. Т.25. №2. С.149-161. DOI: 10.33048/mattrudy.2022.25.206 РИНЦ
Dates:
| Submitted: | Jul 17, 2022 |
| Accepted: | Nov 2, 2022 |
| Published print: | Dec 16, 2022 |
| Published online: | Dec 16, 2022 |
Identifiers:
| Scopus: | 2-s2.0-85144136218 |
| Elibrary: | 58962412 |
| OpenAlex: | W4311897268 |