Simultaneous confidence bands for a class of 2-D spectral estimates

The problem of deriving simultaneous confidence bands for a class of 2-D spectral estimates is considered. Specifically, we consider the class of spectral estimates obtained by fitting 2-D noncausal autoregressive and Gaussian Markov random field models to the given lattice data. In such parametric methods the spectrum is a function of estimates of model parameters. Using the asymptotic normality of the parameter estimates and Scheffe´s projection theorem, simultaneous confidence bands for the estimated spectrum are derived. Supporting computer simulation results are also provided.