Asymptotic Properties of the Least Squares Estimates in a Stationary Random Field

摘要

A particular two dimensional model in a stationary random field, which has a wide applications in statistical signal processing and in texture classifications, is considered. We prove the consistency and also obtain the asymptotic distributions of the least squares estimators of the different model parameters. It is observed that the asymptotic distribution of the least squares estimators are 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.