Electronic Journal of Statistics

Multivariate adaptive warped kernel estimation

Gaëlle Chagny, Thomas Laloë, and Rémi Servien

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We deal with the problem of nonparametric estimation of a multivariate regression function without any assumption on the compacity of the support of the random design. To tackle the problem, we propose to extend a “warping” device to the multivariate framework. An adaptive warped kernel estimator is first defined in the case of known design distribution and proved to be optimal in the oracle sense. Then, a general procedure is carried out: the marginal distributions of the design are estimated by the empirical cumulative distribution functions, and the dependence structure is built using a kernel estimation of the copula density. The copula density estimator is also studied and proved to be optimal in the oracle and in the minimax sense. The plug-in of this estimator in the regression function estimator provides a fully data-driven procedure. A numerical study illustrates the theoretical results.

Article information

Electron. J. Statist., Volume 13, Number 1 (2019), 1759-1789.

Received: October 2017
First available in Project Euclid: 5 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62G08: Nonparametric regression 62H12: Estimation

Creative Commons Attribution 4.0 International License.


Chagny, Gaëlle; Laloë, Thomas; Servien, Rémi. Multivariate adaptive warped kernel estimation. Electron. J. Statist. 13 (2019), no. 1, 1759--1789. doi:10.1214/19-EJS1565. https://projecteuclid.org/euclid.ejs/1559700178

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