Title: Testing parametric regression models when the errors are spatially correlated
Authors: Andrea Meilan-Vila - Universidade da Coruna (Spain) [presenting]
Jean Opsomer - Westat (United States)
Mario Francisco-Fernandez - Universidade da Coruna (Spain)
Rosa Crujeiras - University of Santiago de Compostela (Spain)
Abstract: A common technique in a statistical data analysis is to determine the appropriateness of a parametric model to represent a dataset. As part of this determination, it is advisable to formally test the model, by treating the parametric model as the null hypothesis against an alternative model, and evaluating the probability of obtaining the observed data under the null hypothesis. The choice of the alternative hypothesis model is crucial in this determination. Nonparametric models may be a choice, since they are quite flexible. A spatial stochastic process, which consists of a collection of random variables indexed on a domain of $R^d$, is considered. In this framework, the observed data tend to exhibit an important feature, close observations tend to be more similar than those that are far apart. Therefore, such observations cannot be treated as independent and the dependence structure should be taken into account and properly introduced into the model. In a spatial context, a weighted $L_2-$test comparing nonparametric and parametric spatial regression fits is presented and theoretically studied. The nonparametric multivariate local linear regression estimator is used in this procedure. Additionally, the finite sample performance of the test is addressed by simulation, introducing a bootstrap calibration procedure.