Robust Estimation for Spatial Autoregressive Processes Based on Bounded Innovation Propagation Representations

BRITOS, GRISEL MARIBEL; OJEDA, SILVIA MARÍA

COMPUTATIONAL STATISTICS (ZEITSCHRIFT)

SPRINGER HEIDELBERG

Año: 2019 vol. 34 p. 1315 - 1335

0943-4062

Robust methods havebeen a successful approach to deal with contaminations and noises inimage processing. In this paper, we introduce a new robust method fortwo-dimensional autoregressive models. Our method,called BMM-2D, relies on representing a two-dimensionalautoregressive process with an auxiliary model to attenuate theeffect of contamination (outliers). We compare the performance of ourmethod with existing robust estimators and the least squaresestimator via a comprehensive Monte Carlo simulation study whichconsiders different levels of replacement contamination and windowsizes. The results show that the new estimator is superior to theother estimators, both in accuracy and precision. An application toimage filtering highlights the findings and illustrates how theestimator works in practical applications.