Nonparametric methods for spatial regression. An application to seismic events

Nonparametric regression estimation is a powerful tool to handle multidimensional data. When a dependent data set is analyzed, classical techniques need to be modified to provide useful results. In this work, different approximations to take the spatial dependence into account are exposed. A bandwidth selection technique that adjusts the generalized cross‐validation criterion for the effect of spatial correlation, in the case of bivariate local polynomial regression, is considered. Moreover, a bootstrap algorithm is designed to assess the variability of the estimated spatial maps, and also to estimate the probability of obtaining a response variable larger than or equal to a given threshold, for a specific point. A simulation study checks the validity of the presented approaches in practice. The broad applicability of the procedures is demonstrated on a data set of earthquakes in the Iberian Peninsula. Copyright © 2011 John Wiley & Sons, Ltd.