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.