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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13706 |
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| _version_ | 1866929283087204352 |
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| author | Maissoro, Hassan Patilea, Valentin Vimond, Myriam |
| author_facet | Maissoro, Hassan Patilea, Valentin Vimond, Myriam |
| contents | The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric mean and autocovariance functions estimators that adapt to the regularity and the design, which can be sparse or dense. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive estimation for Weakly Dependent Functional Times Series Maissoro, Hassan Patilea, Valentin Vimond, Myriam Statistics Theory The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric mean and autocovariance functions estimators that adapt to the regularity and the design, which can be sparse or dense. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators. |
| title | Adaptive estimation for Weakly Dependent Functional Times Series |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2403.13706 |