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Article Dans Une Revue Electronic Journal of Statistics Année : 2019

Multivariate adaptive warped kernel estimation

Gaëlle Chagny
Thomas Laloë
Rémi Servien

Résumé

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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Dates et versions

hal-01616373 , version 1 (13-10-2017)
hal-01616373 , version 2 (01-02-2019)

Identifiants

  • HAL Id : hal-01616373 , version 2

Citer

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