Least-squares estimators in a stationary random field

Abstract

A particular two-dimensional model in a stationary random field, which has wide applications in statistical signal processing and texture classifications. is considered. We prove the consistency and also obtain asymptotic distributions of the leastsquares estimators of different model parameters. It is observed that the asymptotic distribution of the least-squares estimators is multivariate normal. Some numerical experiments are performed to see how the asymptotic results work for finite samples. We propose some open problems at the end.