Spectral Approximation to the Likelihood for an Intrinsic Gaussian Random Field

Intrinsic Gaussian random fields generated by conditional autoregressive models are considered. A spectral approximation to the log-likelihood function of an intrinsic random field was given by Künsch. Here a rigorous treatment is given of the comparison between the exact and spectral log-likelihood functions as the domain of observations increases.intrinsic random fields spectral approximation conditional autoregression Whittle approximation trace class norm