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  • 标题:Multivariate adaptive warped kernel estimation
  • 本地全文:下载
  • 作者:Gaëlle Chagny ; Thomas Laloë ; Rémi Servien
  • 期刊名称:Electronic Journal of Statistics
  • 印刷版ISSN:1935-7524
  • 出版年度:2019
  • 卷号:13
  • 期号:1
  • 页码:1759-1789
  • DOI:10.1214/19-EJS1565
  • 语种:English
  • 出版社:Institute of Mathematical Statistics
  • 摘要: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.
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