Asymptotic Spectral Theory for Spatial Data

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