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Article

An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

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Computer Science Department, Technische Universität Darmstadt, 64289 Darmstadt, Germany
2
Computer Science Department, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
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Author to whom correspondence should be addressed.
Received: 30 October 2020 / Revised: 12 December 2020 / Accepted: 25 December 2020 / Published: 30 December 2020
(This article belongs to the Section Regression Models)
The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt’s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed. View Full-Text
Keywords: nonparametric regression; Nadaraya-Watson kernel regression; bias nonparametric regression; Nadaraya-Watson kernel regression; bias
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MDPI and ACS Style

Tosatto, S.; Akrour, R.; Peters, J. An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions. Stats 2021, 4, 1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010001

AMA Style

Tosatto S, Akrour R, Peters J. An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions. Stats. 2021; 4(1):1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010001

Chicago/Turabian Style

Tosatto, Samuele, Riad Akrour, and Jan Peters. 2021. "An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions" Stats 4, no. 1: 1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010001

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