Kernel Inverse Regression for spatial random fields
Statistics Theory
2008-12-18 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.0812.3254,
title = {Kernel Inverse Regression for spatial random fields},
author = {Jean-Michel Loubes and Anne-Françoise Yao},
journal= {arXiv preprint arXiv:0812.3254},
year = {2008}
}