Tosatto, Samuele ; Akrour, Riad ; Peters, Jan (2024)
An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions.
In: Stats, 2020, 4 (1)
doi: 10.26083/tuprints-00017437
Artikel, Zweitveröffentlichung, Verlagsversion
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Tosatto, Samuele ; Akrour, Riad ; Peters, Jan |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions |
| Sprache: | Englisch |
| Publikationsjahr: | 15 Januar 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2020 |
| Ort der Erstveröffentlichung: | Basel |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Stats |
| Jahrgang/Volume einer Zeitschrift: | 4 |
| (Heft-)Nummer: | 1 |
| Kollation: | 17 Seiten |
| DOI: | 10.26083/tuprints-00017437 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/17437 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | nonparametric regression, Nadaraya-Watson kernel regression, bias |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-174378 |
| Zusätzliche Informationen: | This article belongs to the Section Regression Models |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik 300 Sozialwissenschaften > 310 Allgemeine Statistiken 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Intelligente Autonome Systeme |
| Hinterlegungsdatum: | 15 Jan 2024 13:47 |
| Letzte Änderung: | 18 Jan 2024 12:42 |
| PPN: | |
| Zugehörige Links: | |
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