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

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An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes. / Boshnakov, Georgi; Das, Sourav; Subba Rao, Tata.

In: Communications in Statistics: Simulation and Computation, Vol. 49, No. 7, 01.07.2020, p. 1839-1854.

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Boshnakov, Georgi ; Das, Sourav ; Subba Rao, Tata. / An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes. In: Communications in Statistics: Simulation and Computation. 2020 ; Vol. 49, No. 7. pp. 1839-1854.

Bibtex

@article{253cf0969f0a43059352dc6eec600a6e,
title = "An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes",
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.",
keywords = "Cross-validation kriging, Mat{\'e}rn class, Variance stabilization, Wave variogram",
author = "Georgi Boshnakov and Sourav Das and {Subba Rao}, Tata",
year = "2020",
month = jul,
day = "1",
doi = "10.1080/03610918.2018.1508698",
language = "English",
volume = "49",
pages = "1839--1854",
journal = "Communications in Statistics: Simulation and Computation",
issn = "0361-0918",
publisher = "Taylor & Francis",
number = "7",

}

RIS

TY - JOUR

T1 - An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes

AU - Boshnakov, Georgi

AU - Das, Sourav

AU - Subba Rao, Tata

PY - 2020/7/1

Y1 - 2020/7/1

N2 - 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.

AB - 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.

KW - Cross-validation kriging

KW - Matérn class

KW - Variance stabilization

KW - Wave variogram

U2 - 10.1080/03610918.2018.1508698

DO - 10.1080/03610918.2018.1508698

M3 - Article

VL - 49

SP - 1839

EP - 1854

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

SN - 0361-0918

IS - 7

ER -