Kernel Inverse Regression for spatial random fields
Abstract
In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the 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 inverse regression. Then, we study, under strong mixing condition, the weak and strong consistency of this estimate, using a kernel estimate of the 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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