On nonparametric inference for spatial regression models under domain expanding and infill asymptotics

Abstract

In this paper, we develop nonparametric inference on spatial regression models as an extension of Lu and Tjøstheim (2014), which develops nonparametric inference on density functions of stationary spatial processes under domain expanding and infill (DEI) asymptotics. In particular, we derive multivariate central limit theorems of mean and variance functions of nonparametric spatial regression models. Built upon those results, we propose a method to construct confidence bands for mean and variance functions.