Empirical Likelihood Ratio Tests for Varying Coefficient Geo Models

Abstract

In this paper, we investigate the varying coefficient models for spatial data distributed over two-dimensional domains.First, the univariate components and the geographical component in the model are approximated via univariate polynomial splines and bivariate penalized splines over triangulation, respectively.The spline estimators of the univariate and bivariate functions are consistent, and their convergence rates are also established.Second, we propose the empirical likelihood based test procedures to conduct both pointwise and simultaneous inferences for the varying coefficient functions.The asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses.The proposed methods also perform favorably in finite sample applications, as we demonstrate them in simulations and an application to an adult obesity prevalence data in the United States.