2-D SPECTRUM ESTIMATION FOR IMPERFECTLY OBSERVED LATTICE DATA.

The use of parametric models and robustified maximum likelihood (ML) to estimate two-dimensional power spectra from imperfectly observed lattice data is investigated. The ML estimates for the signal-plus-noise model are consistent and asymptotically efficient for noncausal autoregressive (NCAR) models, but the solution requires the use of computationally expensive nonlinear optimization, such as Newton-Raphson. By approximating the ML equations through the use of a toroidal lattice the computational complexity is reduced without unduly destroying the asymptotic properties of the estimates. When outliers in the data occur, ML might not perform well. In this case the authors make no strict assumption about the distribution of the observations but assume only that the data are nominally Gaussian but with heavier tails. Then they use a robust procedure to estimate the parameters for the model.