Asymptotic Properties of Three Alternative Estimators of Spatial Parameters

Parameters of Gaussian spatial models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical for large data sets. We study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, which are meant to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.