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Title: Spatial prediction based on kernel method and dimension reduction Authors:  Anne Francoise Yao - Universite Clermont Auvergne/LMBP (France) [presenting]
Liliana Forzani - Universidad Nacional del Litoral (Argentina)
Maria Antonella Gieco - CONICET - Facultad de Ingenieria Quimica, UNL (Argentina)
Pamela Llop - Facultad de Ingenieria Quimica, UNL-CONICET (Argentina)
Abstract: The problem of regression (or prediction) is a main concern when dealing with spatial data modelling. In this framework, kriging (and related linear or spatial generalized linear model) is a well-known and widely used method. However, krigging is suitable mainly when dealing with the spatial Gaussian process. In the case of non-Gaussian process, some alternatives have been proposed. Among them, the spatial kernel approach which is the subject of a large and dynamic literature of the last years. We are interested in the problem of predicting unknown spatial values of the process using both dependence information due to the spatial location on one hand, and to some exogenous variables on the other hand. In this setting, in some non-Gaussian cases, the kernel approaches outperform the krigging methods, but with small difference in the prediction errors. As a solution, we suggest combining the spatial kernel predictors with a dimension reduction methods. Then, we study this new spatial predictor. We illustrate our purpose through some simulations.