Comparing spatial dependence structures using spectral density estimators

Abstract

AbstractThe aim of this work is to establish statistical methodology in order to analyze changes in the dependence structure for different spatial processes or for a process observed on a regular grid at different time moments. We propose a test statistic for testing the hypothesis $H_0:f_1=f_2$, where each $f_l$ denotes the spectral density of each process, for $l=1,2$. The test is based on a Cramer‐von‐Mises functional type test introduced in (Vilar‐Fernández and Gonzálex‐Manteiga, 2004) for the regression context. The study is developed for $L=2$, but generalizations to $L>2$ are straightforward. The application of our technique is related to biomonitoring studies which have been carried out in order to determine levels of heavy metal concentrations, taking mosses as biomonitors. Copyright © 2007 John Wiley & Sons, Ltd.