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Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics
Abstract
It is shown that in model-based geostatistics, not all parameters in the Matérn 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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Statistical Modeling of Spatial Extremes
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Matérn Cross-Covariance Functions for Multivariate Random Fields
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Geostatistical Inference Under Preferential Sampling
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Metadata
- Authors
- Zhang, H.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2004-03
- Volume
- 99
- Issue
- 465
- Pages
- 250-261
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2040635790
- Cited by
- 584
- References
- 30
- FWCI
- 22.92
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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