Empirical robust estimators for 2D noncausal autoregressive models

Some robust estimators are suggested for two-dimensional (2D) noncausal autoregressive models. These estimators are based on the general theme that robust estimators are characterized by a mechanism that down-weights data which seem extreme relative to the aggregate data. Although there could be many schemes to accomplish this down-weighting, resulting estimates should be consistent and efficient, or nearly so. Two classes of robust estimators are presented. The first class uses robust covariance estimates in place of sample covariance estimates, while the second class embodies the idea that bounding the influence of outlying data produces robustness. Simulation results are included to demonstrate the usefulness of these estimators