  In the last years there has been a growing interest in proposing methods for
estimating covariance functions for geostatistical data. Among these, maximum
likelihood estimators have nice features when we deal with a Gaussian model.
However maximum likelihood becomes impractical when the number of observations
is very large. In this work we review some solutions and we contrast them in
terms of loss of statistical efficiency and computational burden. Specifically
we focus on three types of weighted composite likelihood functions based on
pairs and we compare them with the method of covariance tapering. Asymptotics
properties of the three estimation methods are derived. We illustrate the
effectiveness of the methods through theoretical examples, simulation
experiments and by analysing a data set on yearly total precipitation anomalies
at weather stations in the United States.
