Approximate ML and REML estimation for regression models with spatial or time series AR(1) noise

Abstract

This paper considers maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of regression models with two-dimensional spatial or one-dimensional time series autoregressive AR(1) noise. Although the exact ML and REML procedures are described, the aim is to develop and present a simple estimation procedure that provides very accurate approximations to the ML and REML estimators and is computationally convenient. An approximation for the bias of the ML estimator of the AR parameters is also investigated. Simulation results are provided to assess the accuracy of our approximations.