A note on computational issues associated with restricted maximum likelihood estimation of covariance rarameters

Abstract

Geostatistical investigations often require that the covariance of a Gussian random field be estimated from a single and discrete realization of the field. If this estimation problem is placed in a restricted maximum likelihood Reml framework, then teh need to construct an appropriate mean filtering matrix arises. In this paper we show that depending on the choice of the mean filtering matrix, the Reml function i may be overly sensitive to round-off errors, ii may require expensive matrix-matrix multiplications, and iii may not retain computationally exploitable structures present in the field covariance matrix. Against this background, we invoke a form of the Reml function that does not depend explicity on any filtering matrix so that the difficulties i, ii, and iii mentioned above do not arise.