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Multivariate adaptive warped kernel estimation

Abstract : 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, thanks to a " warping " device. 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 proved to be optimal in the oracle and in the minimax sense. The plug-in of these estimates in the regression function estimator provides a fully data-driven estimate. A numerical study illustrates the theoretical results.
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Contributor : Gaëlle Chagny <>
Submitted on : Friday, February 1, 2019 - 2:37:49 PM
Last modification on : Tuesday, June 1, 2021 - 10:48:04 PM
Long-term archiving on: : Thursday, May 2, 2019 - 10:00:28 PM


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  • HAL Id : hal-01616373, version 2


Gaëlle Chagny, Thomas Laloë, Rémi Servien. Multivariate adaptive warped kernel estimation. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2019, 13 (1), pp.1759-1789. ⟨hal-01616373v2⟩



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