Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [42 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01616373
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

File

Chagny_Laloe_Servien_Hal_rev.p...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01616373, version 2

Citation

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⟩

Share

Metrics

Record views

150

Files downloads

368