Mixed-spectra analysis for stationary random fields

We consider a, discrete time, weakly stationary bidimensional process, for which the spectral measure is the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. In this paper we are interested in estimating the spectral density of the absolutely continuous measure and of the density on the lines. For this aim, by using the double kernel method, we construct consistent estimators of these densities and we study their asymptotic behaviors in term of the mean squared error with rate.