Kernel Inverse Regression for spatial random fields

Jean-Michel Loubes (1) , Anne-Françoise Yao (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMGEM - Laboratoire de MicrobiologiE de Géochimie et d'Ecologie Marines

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.

Mots clés: Kernel estimator; Spatial regression; Random fields; Strong mixing coefficient; Dimension reduction; Inverse Regression

Domaines: Statistiques [math.ST]

Jean-Michel Loubes, Anne-Françoise Yao. Kernel Inverse Regression for spatial random fields. 2008. ⟨hal-00347813⟩