A simulation comparison of estimators of spatial covariance parameters and associated bootstrap percentiles

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Title: A simulation comparison of estimators of spatial covariance parameters and associated bootstrap percentiles
Authors: Kelly, Gabrielle E.
Menezes, Raquel
Permanent link: http://hdl.handle.net/10197/10492
Date: Sep-2018
Online since: 2019-05-16T09:56:37Z
Abstract: A simulation study is implemented to study estimators of the covariance structure of a stationary Gaussian spatial process and a spatial process with t-distributed margins. The estimators compared are Gaussian restricted maximum likelihood (REML) and curve-fitting by ordinary least squares and by the nonparametric Shapiro-Botha approach. Processes with Matérn covariance functions are considered and the parameters estimated are the nugget, partial sill and practical range. Both parametric and nonparametric bootstrap distributions of the estimators are computed and compared to the true marginal distributions of the estimators. Gaussian REML is the estimator of choice for both Gaussian and t-distributed data and all choices of the Matérn covariance structure. However, accurate estimation of the Matérn shape parameter is critical to achieving a good fit while this does not affect the Shapiro-Botha estimator. The parametric bootstrap performed well for all estimators although it tended to be biased downward. It was slightly better than the nonparametric bootstrap for Gaussian data, equivalent to it for t-distributed data and worse overall for the Shapiro-Botha estimates. A numerical example, obtained from environmental monitoring, is included to illustrate the application of the methods and the bootstrap.
Type of material: Journal Article
Publisher: UCLA Department of Statistics
Journal: Journal of Environmental Statistics
Volume: 8
Issue: 6
Start page: 1
End page: 21
Copyright (published version): 2017 the Authors
Keywords: Gaussian random fieldVariogramRestricted maximum likelihoodVariogram curve-fittingShapiro-Botha estimationSpatial bootstrap
Other versions: http://www.jenvstat.org/v08/i06
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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