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Stats, Volume 4, Issue 1
March 2021 - 16 articles
Cover Story: The Nadaraya–Watson kernel estimator is among the most popular non-parameteric regression techniques thanks to its simplicity. Its asymptotic bias was studied by Rosenblatt in 1969 and has been reported in several related works. However, its asymptotic nature gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making increases the need for hard guarantees. To alleviate this issue, a novel non-probabilistic upper bound of the bias is proposed, which relies on Lipschitz assumptions and mitigates some of Rosenblatt’s analysis prerequisites. The upper bound holds for a large class of kernels, designs, regression functions, admits finite bandwidths, and is tight even with large second derivatives of the regression function—where Rosenblatt’s analysis typically fails. View this paper
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Stats - ISSN 2571-905X