%0 Unpublished work
%T Kernel Inverse Regression for spatial random fields
%+ Institut de Mathématiques de Toulouse UMR5219 (IMT)
%+ Laboratoire de MicrobiologiE de Géochimie et d'Ecologie Marines (LMGEM)
%A Loubes, Jean-Michel
%A Yao, Anne-Françoise
%8 2008-12-16
%D 2008
%Z 0812.3254
%K Kernel estimator
%K Spatial regression
%K Random fields
%K Strong mixing coefficient
%K Dimension reduction
%K Inverse Regression
%Z Mathematics [math]/Statistics [math.ST]Preprints, Working Papers, ...
%X In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the matrix of covariance of the expectation of the explanatory given the dependent variable, called the \emph{inverse regression}. Then, we study, under strong mixing condition, the weak and strong consistency of this estimate, using a kernel estimate of the \emph{inverse regression}. We provide the asymptotic behaviour of this estimate. A spatial predictor based on this dimension reduction approach is also proposed. This latter appears as an alternative to the spatial non-parametric predictor.
%G English
%2 https://hal.science/hal-00347813/document
%2 https://hal.science/hal-00347813/file/Loubes-Yao.pdf
%L hal-00347813
%U https://hal.science/hal-00347813
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-AMU
%~ INSA-TOULOUSE
%~ IMT
%~ LMGEM
%~ UT1-CAPITOLE
%~ INSA-GROUPE
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP