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On maximum likelihood estimation of parameters in incorrectly specified models of covariance for spatial data
Authors:A J Watkins and F H M Al-Boutiahi
Institution:(1) Department of Management Science and Statistics, University College of Swansea, Singleton Park, SA2 8PP Swansea, United Kingdom
Abstract:The analysis of, and from, models of spatial data usually proceeds under the assumption, often implicit, that the correct model has been specified. However, any model identification procedures based on sample data are subject to error, and consequences of such errors then permeate subsequent analysis. Thus, an attempt to quantify some of these consequences is of interest. A standard framework for analysis is extended here, by introduction of information theory, to permit the study of effects of model misspecification on maximum likelihood estimators of parameters of model covariance. Asymptotically valid theoretical results are presented, and the relevance of these results to samples of finite sizes met in practice is assessed in a series of simulation experiments. The effect of model misspecification, and use of estimators of parameters of misspecified covariance models, on the practical problem of prediction at a previously unsampled location is considered briefly, and further areas for possible investigation are outlined.
Keywords:information theory  multidimensional normality  profile log-likelihood  prediction  simulation  statistical inference
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