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. 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.
Citation
Gaëlle Chagny. Thomas Laloë. Rémi Servien. "Multivariate adaptive warped kernel estimation." Electron. J. Statist. 13 (1) 1759 - 1789, 2019. https://doi.org/10.1214/19-EJS1565