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arXiv · 0812.3254

Kernel Inverse Regression for spatial random fields

Jean-Michel Loubes·Anne-Françoise Yao
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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.

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Jean-Michel Loubes, Anne-Françoise Yao. 2008-12-17. Kernel Inverse Regression for spatial random fields. https://arxiv.org/abs/0812.3254

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