MLREML4 - A PROGRAM FOR THE INFERENCE OF THE POWER VARIOGRAM MODEL BYMAXIMUM-LIKELIHOOD AND RESTRICTED MAXIMUM-LIKELIHOOD

The power variogram model gamma(h) = alpha.\h\(beta), alpha > 0, beta epsilon]0, 2[, is an important theoretical model when only the intrins ic hypothesis is assumed for a random function and has been extensivel y used in practice, e.g, for variables such as piezometric level in gr oundwater hydrology and rainfall in surface hydrology. MLREML4 is an A NSI FORTRAN-77 program which provides maximum likelihood and restricte d maximum likelihood estimates of the parameters alpha and beta of the model, parameters of scale and shape, respectively. These parametric estimators have several advantages over other non-parametric estimator s: the former are more efficient (as will be shown using the sampling distribution of the estimates), with only the parameters of interest b eing estimated (instead of estimating the variogram for different dist ances and fitting the model). Furthermore the uncertainty of the estim ates is easily assessed by their standard errors, which means approxim ate confidence limits may be constructed. A good strategy is to use th e non-parametric and the parametric approach complementarily. Firstly the non-parametric approach suggests which is the kind of variogram mo del that seems more adequate and secondly, the parameters are estimate d by the parametric approach. Results from simulation and different se ts of data are shown to illustrate the implementation of the program. MLREML4 is an upgrade of MLREML, i.e. it has all the capabilities of t he latter plus the possibility of choosing the power variogram model, in addition to the three transition models, spherical, exponential and Gaussian, already included in MLREML. (C) 1998 Elsevier Science Ltd. All rights reserved