Performance of Robust RA Estimator for Bidimensional Autoregressive Models

Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations

“…Finally the RA estimators were implemented according to the details formulated in [25]. To facilitate the paper reading, only the boxplots of the simulations have been included in the body of the work; the numerical Monte Carlo results are shown in the Appendix.…”

“…The following proposals outline some directions for future work. In [25], the author established the asymptotic normality and consistency of the robust RA estimator for the parameter φ of a two-dimensional autoregressive process. Although the estimators M, GM and BMM are reasonable to estimate parameter φ, their asymptotic behavior is still an open problem.…”

“…Robust estimators have been defined for models with a small amount of parameters. Here, we summarize the well-known robust estimators for the model (3); however, a more general development can be found for the AR and MA models in [20], [3], [27], [41] and [13].…”

“…In [27], the authors presented the robust autocovariance (RA) estimator for AR-2D processes which was first defined for time series models by [12]. This estimator is determined by the following equations ∞ k,l,r=0…”

“…The robust estimators of Residual Autocovariance (RA) were presented by [12] in the context of the time series, where in the procedure of recursive estimation the residues are cleaned through the application of a robust function. The extension of the RA estimators for two-dimensional autoregressive models and their corresponding computational treatment were developed by [27]. Monte Carlo simulation studies show that the performance of the RA estimator is higher than the M estimator and slightly better than the GM estimator when the model has been contaminated with additive type outliers.…”