Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 99, Issue 465, Pages 250-261Publisher
TAYLOR & FRANCIS INC
DOI: 10.1198/016214504000000241
Keywords
equivalent measures; generalized linear mixed model; Kriging; Matern class; minimum mean squared error; model-based; geostatistics; prediction
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it is shown that in model-based geostatistics, not all parameters in the Matern class can be estimated consistently if data are observed in an increasing density in a fixed domain, regardless of the estimation methods used. Nevertheless, one quantity can be estimated consistently by the maximum likelihood method, and this quantity is more important to spatial interpolation. The results are established by using the properties of equivalence and orthogonality of probability measures. Some sufficient conditions are provided for both Gaussian and non-Gaussian equivalent measures, and necessary conditions are provided for Gaussian equivalent measures. Two simulation studies are presented that show that the fixed-domain asymptotic properties can explain some finite-sample behavior of both interpolation and estimation when the sample size is moderately large.
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