Asymptotic Spectral Theory for Spatial Data

TL;DR

This paper develops the asymptotic spectral theory for stationary spatial data, analyzing Fourier coefficients, periodograms, and spectral density estimators, with applications to both linear and nonlinear fields.

Contribution

It provides new asymptotic results for spectral analysis of stationary random fields, including limiting distributions and consistency of estimators under mild conditions.

Findings

Limiting distributions of Fourier coefficients derived

Uniform consistency of spectral density estimators established

Results applicable to both linear and nonlinear spatial fields

Abstract

In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of Fourier coefficients, and the uniform consistency of kernel spectral density estimators are obtained under various mild conditions on moments and dependence structures. The validity of the aforementioned asymptotic results for estimated spatial fields is also established.