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arXiv · 2503.15039

A Note on Local Linear Regression for Time Series in Banach Spaces

Florian Heinrichs
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Abstract

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.

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Florian Heinrichs. 2025-03-19. A Note on Local Linear Regression for Time Series in Banach Spaces. https://arxiv.org/abs/2503.15039

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