Asymptotic behavior of RA-estimates in autoregressive 2D processes

BUSTOS, O.H., RUIZ, M., OJEDA, S., VALLEJOS, R., FRERY, A.

JOURNAL OF STATISTICAL PLANNING AND INFERENCE

ELSEVIER SCIENCE BV

Año: 2009 vol. 139 p. 3649 - 3664

0378-3758

In this work we study the asymptotic behavior of a robust class of estimators of the coefficient of a AR-2D process. We establish the precise conditions for the consistency and asymptotic normality of the RA estimator. The AR-2D model has many applications in image modeling and statistical image processing, therefore the relevance of knowing such properties. The adequacy of the AR-2D model is analyzed with real images; we also show the impact of contamination and the capability of the RA estimator to produce useful results even in the presence of spurious data.