An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes

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In many fields of science dealing with geostatistical data, the weighted least squares proposed by Cressie (1985) remains a popular choice for variogram estimation. Simplicity, ease of implementation and non-parametric nature are its principle advantages. It also avoids the heavy computational burden of Generalized least squares. But that comes at the cost of loss of information due to the use of a diagonal weight matrix. Besides, the parameter dependent weight matrix makes the estimating equations biased. In this paper we propose two alternative weight matrices which do not depend on the parameters. We show that one of the weight matrices gives parameter estimates with lower asymptotic variance and also has asymptotically unbiased estimating equations. The observations are validated using simulation and real data.

Bibliographical metadata

Original languageEnglish
Pages (from-to)1839-1854
Number of pages16
JournalCommunications in Statistics: Simulation and Computation
Issue number7
Early online date10 Nov 2018
Publication statusPublished - 1 Jul 2020

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