Asymptotic properties of BMM-estimator in bidimensional autoregressive processes

Abstract

In this work, we present the BMM 2D estimator, a robust estimator for the parameters of the bidimensional autoregressive model (AR-2D model). The new estimator is a two-dimensional extension of the BMM estimator for the parameters of the autoregressive models used in time series analysis. We demonstrate that the BMM 2D estimator is consistent and asymptotically normal, which provides a valuable tool to carry out inferential studies about the parameters of the AR-2D model. Also, we show the performance of the BMM 2D estimator compared with the least-squares estimator and illustrate it in the context of image restoration problems.