Nonparametric Inference for Regression Models with Spatially Correlated Errors

Resumen

Regression estimation can be approached using nonparametric procedures, producing exible estimators and avoiding misspeci cation problems. Alternatively, parametric methods may be preferable to nonparametric approaches if the regression function belongs to the assumed parametric family. However, a bad speci cation of this family can lead to wrong conclusions. Regression function misspeci cation problems can be somewhat tackled by applying a goodness-of- t test. For data presenting some kind of complexity, for example, circular data, the approaches used in regression estimation or in goodness-of- t tests have to be conveniently adapted. Moreover, it might occur that the variables of interest can present a certain type of dependence. For example, they can be spatially correlated, where observations which are close in space tend to be more similar than observations that are far apart. The goal of this thesis is twofold, rst, some inference problems for regression models with Euclidean response and covariates, and spatially correlated errors are analyzed. More speci - cally, a testing procedure for parametric regression models in the presence of spatial correlation is proposed. The second aim is to design and study new approaches to deal with regression function estimation and goodness-of- t tests for models with a circular response and an Rd-valued covariate. In this setting, nonparametric proposals to estimate the circular regression function are provided and studied, under the assumption of independence and also for spatially correlated errors. Moreover, goodness-of- t tests for assessing a parametric regression model are presented in these two frameworks. Comprehensive simulation studies and application of the different techniques to real datasets complete this dissertation.