Asymptotics for REML estimation of spatial covariance parameters

In agricultural field trials, restricted maximum likelihood estimation (REML) of the spatial covariance parameters is often preferred to maximum likelihood. Although it has either been conjectured or assumed that REML estimators are asymptotically Gaussian, conditions under which such asymptotic results hold are clearly needed. This article gives checkable conditions for spatial regression when sampling locations are either on a rectangular grid or are irregularly spaced but satisfy certain growth conditions.