A Note on Local Linear Regression for Time Series in Banach Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908275039010816 |
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| author | Heinrichs, Florian |
| author_facet | Heinrichs, Florian |
| contents | This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya-Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on Local Linear Regression for Time Series in Banach Spaces Heinrichs, Florian Statistics Theory Methodology 62G08, 62M10, 62R10 This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya-Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects. |
| title | A Note on Local Linear Regression for Time Series in Banach Spaces |
| topic | Statistics Theory Methodology 62G08, 62M10, 62R10 |
| url | https://arxiv.org/abs/2503.15039 |