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

Samuele Tosatto, Riad Akrour and Jan Peters
Additional contact information
Samuele Tosatto: Computer Science Department, Technische Universität Darmstadt, 64289 Darmstadt, Germany
Riad Akrour: Computer Science Department, Technische Universität Darmstadt, 64289 Darmstadt, Germany
Jan Peters: Computer Science Department, Technische Universität Darmstadt, 64289 Darmstadt, Germany

Stats, 2020, vol. 4, issue 1, 1-17

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.

Keywords: nonparametric regression; Nadaraya-Watson kernel regression; bias (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2571-905X/4/1/1/pdf (application/pdf)
https://www.mdpi.com/2571-905X/4/1/1/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:4:y:2020:i:1:p:1-17:d:470489

Access Statistics for this article

Stats is currently edited by Mrs. Minnie Li

More articles in Stats from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().