Asymptotic properties of the least squares estimators of a two dimensional model

Abstract.

We consider a particular two dimensional model, which has a wide applications in statistical signal processing and texture classifications. We prove the consistency of the least squares estimators of the model parameters and also obtain the asymptotic distribution of the least squares estimators. We observe the strong consistency of the least squares estimators when the errors are independent and identically distributed double array random variables. We show that the asymptotic distribution of the least squares estimators are multivariate normal. It is observed that the asymptotic dispersion matrix coincides with the Cramer-Rao lower bound. This paper generalizes some of the existing one dimensional results to the two dimensional case. Some numerical experiments are performed to see how the asymptotic results work for finite samples.