Asymptotic Spectral Theory for Spatial Data

In this paper, we study the asymptotic theory for spectral analysis of stationary random fields on Z(2), 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.