INFERENCE OF SPATIAL INDICATOR COVARIANCE PARAMETERS BY MAXIMUM-LIKELIHOOD USING MLREML

This paper discusses an application of a previously published code to show how maximum likelihood estimation may be used for the inference o f spatial indicator covariance parameters. Although the maximum likeli hood equations are derived on the assumption of a multivariate normal distribution for the experimental data, when the data are neither Gaus sian nor can be transformed to normal scores (as is clearly the case w ith indicator data) maximum likelihood still provides a weighted least squares criterion of fitting spatial covariance models. The estimator is still consistent, asymptotically unbiased and the estimates are as ymptotically normally distributed. Maximum likelihood also provides th e uncertainty of the estimates by assessing the standard errors of the estimates. The method is recommended for cases in which the number of experimental data is relatively small (several dozens) and irregularl y distributed. In such situations, the experimental indicator variogra m, calculated by classical non-parametric methods, is so noisy that it is extremely difficult to fit it to a model. This difficulty increase s as the threshold moves further away from the median of the data. A s imulated case study is used to demonstrate the application of the meth od and illustrate the results. The program MLREML (previously publishe d in Computers and Geosciences) has been used ro perform maximum likel ihood estimation of spatial indicator covariances. (C) 1998 Elsevier S cience Ltd. All rights reserved.