Abstract
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.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
We derive an upper bound of the bias of the Nadaraya-Watson kernel regression that is valid for a large class of design and for any choice of bandwidth
Its asymptotic bias and variance are well-known in the literature
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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