Inference for variograms

Bowman, A.W. and Crujeiras, R.M. (2013) Inference for variograms. Computational Statistics and Data Analysis, 66, pp. 19-31. (doi:10.1016/j.csda.2013.02.027)

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Abstract

The empirical variogram is a standard tool in the investigation and modelling of spatial covariance. However, its properties can be difficult to identify and exploit in the context of exploring the characteristics of individual datasets. This is particularly true when seeking to move beyond description towards inferential statements about the structure of the spatial covariance which may be present. A robust form of empirical variogram based on a fourth-root transformation is used. This takes advantage of the normal approximation which gives an excellent description of the variation exhibited on this scale. Calculations of mean, variance and covariance of the binned empirical variogram then allow useful computations such as confidence intervals to be added to the underlying estimator. The comparison of variograms for different datasets provides an illustration of this. The suitability of simplifying assumptions such as isotropy and stationarity can then also be investigated through the construction of appropriate test statistics and the distributional calculations required in the associated p-values can be performed through quadratic form methods. Examples of the use of these methods in assessing the form of spatial covariance present in datasets are shown, both through hypothesis tests and in graphical form. A simulation study explores the properties of the tests while pollution data on mosses in Galicia (North-West Spain) are used to provide a real data illustration.

Item Type:Articles
Additional Information:NOTICE: this is the author’s version of a work that was accepted for publication in Computational Statistics and Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bowman, Professor Adrian
Authors: Bowman, A.W., and Crujeiras, R.M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Computational Statistics and Data Analysis
Publisher:Elsevier B.V.
ISSN:0167-9473
Published Online:26 March 2013
Copyright Holders:Copyright © 2013 Elsevier B.V.
First Published:First published in Computational Statistics and Data Analysis 66:19-31
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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