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

Georgi Boshnakov, Sourav Das, Tata Subba Rao

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    Abstract

    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.
    Original languageEnglish
    Pages (from-to)1839-1854
    Number of pages16
    JournalCommunications in Statistics: Simulation and Computation
    Volume49
    Issue number7
    Early online date10 Nov 2018
    DOIs
    Publication statusPublished - 1 Jul 2020

    Keywords

    • Cross-validation kriging
    • Matérn class
    • Variance stabilization
    • Wave variogram

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