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

Abstract

Robust methods have been a successful approach for dealing with contamination and noise in the context of spatial statistics and, in particular, in image processing. In this paper, we introduce a new robust method for spatial autoregressive models. Our method, called BMM-2D, relies on representing a two-dimensional autoregressive process with an auxiliary model to attenuate the effect of contamination (outliers). We compare the performance of our method with existing robust estimators and the least squares estimator via a comprehensive Monte Carlo simulation study, which considers different levels of replacement contamination and window sizes. The results show that the new estimator is superior to the other estimators, both in accuracy and precision. An application to image filtering highlights the findings and illustrates how the estimator works in practical applications.