Open Access
2021 On a Nadaraya-Watson estimator with two bandwidths
Fabienne Comte, Nicolas Marie
Author Affiliations +
Electron. J. Statist. 15(1): 2566-2607 (2021). DOI: 10.1214/21-EJS1849

Abstract

In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for both data driven estimators and for the resulting ratio. The simulation study confirms that both estimators have good performances, compared to the ones obtained by cross-validation selection of the bandwidth. However, unexpectedly, the single-bandwidth cross-validation estimator is found to be much better than the ratio of the previous two good estimators, in the small noise context. However, the two methods have similar performances in models with large noise.

Citation

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Fabienne Comte. Nicolas Marie. "On a Nadaraya-Watson estimator with two bandwidths." Electron. J. Statist. 15 (1) 2566 - 2607, 2021. https://doi.org/10.1214/21-EJS1849

Information

Received: 1 January 2020; Published: 2021
First available in Project Euclid: 5 May 2021

Digital Object Identifier: 10.1214/21-EJS1849

Subjects:
Primary: 62G08
Secondary: 62G05

Keywords: Bandwidth selection , Nonparametric kernel estimator , quotient estimator , regression model

Vol.15 • No. 1 • 2021
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