In this thesis, parametric techniques using noncausal spatial models are given. In parametric techniques, the spectrum estimation problem can be divided into two parts, one to estimate the model order and the other to estimate the model parameters characterizing the model. These models characterize the statistical dependence of the observation at location at s on its neighbors in all directions. Existence and uniqueness properties of the ML estimates have the following interesting correlation matching property.
Confidence regions are an important part of any point estimation scheme.
Using the asymptotic normality property of the ML estimates, simultaneous confidence bands for estimated GMRF spectrum are derived. Some decision rules for choosing appropriate GMRF models are also discussed. The driving noise in GMRF models is a correlated noise sequence. Some times it is more appropriate to model the driving noise as white noise sequence. In this case one obtains SAR model.