Maximum likelihood estimation of mean functions for Gaussian processes under small noise asymptotics
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916832077676544 |
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| author | Kobayashi, Mitsuki Nishiwaki, Yuto Shimizu, Yasutaka Takaoka, Nobutoki |
| author_facet | Kobayashi, Mitsuki Nishiwaki, Yuto Shimizu, Yasutaka Takaoka, Nobutoki |
| contents | Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be written explicitly. When it is subjected to a small noise asymptotic condition leading to the vanishing of the primary Gaussian noise, we attain local asymptotic normality results, accompanied by insights into the asymptotic efficiency of these estimators. In addition, we introduce M-estimators based on discrete samples, which also leads us to the asymptotic efficiency. Furthermore, we provide quasi-information criteria for model selection analogous to Akaike Information Criteria in discretely observed cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood estimation of mean functions for Gaussian processes under small noise asymptotics Kobayashi, Mitsuki Nishiwaki, Yuto Shimizu, Yasutaka Takaoka, Nobutoki Statistics Theory 60G15, 62F12 Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be written explicitly. When it is subjected to a small noise asymptotic condition leading to the vanishing of the primary Gaussian noise, we attain local asymptotic normality results, accompanied by insights into the asymptotic efficiency of these estimators. In addition, we introduce M-estimators based on discrete samples, which also leads us to the asymptotic efficiency. Furthermore, we provide quasi-information criteria for model selection analogous to Akaike Information Criteria in discretely observed cases. |
| title | Maximum likelihood estimation of mean functions for Gaussian processes under small noise asymptotics |
| topic | Statistics Theory 60G15, 62F12 |
| url | https://arxiv.org/abs/2507.05628 |