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

TL;DR

This paper extends nonparametric inference methods for spatial regression models under domain expanding and infill asymptotics, deriving central limit theorems and proposing confidence band construction techniques.

Contribution

It develops multivariate CLTs for mean and variance functions in spatial regression and introduces a new method for confidence band construction.

Findings

Derived multivariate central limit theorems for spatial regression functions

Proposed a novel approach for constructing confidence bands

Extended nonparametric inference to spatial models under DEI asymptotics

Abstract

In this paper, we develop nonparametric inference on spatial regression models as an extension of Lu and Tj\ostheim(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.