Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function
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ArticleAuthors
Yan, Yuan
Genton, Marc G.

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program
Date
2017-07-12Online Publication Date
2017-07-12Print Publication Date
2018-08Permanent link to this record
http://hdl.handle.net/10754/625682
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Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.Citation
Yan Y, Genton MG (2017) Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function. Environmetrics: e2458. Available: http://dx.doi.org/10.1002/env.2458.Sponsors
This research was supported by the King Abdullah University of Science and Technology (KAUST).Publisher
WileyJournal
EnvironmetricsDOI
10.1002/env.2458Additional Links
http://onlinelibrary.wiley.com/doi/10.1002/env.2458/abstractae974a485f413a2113503eed53cd6c53
10.1002/env.2458
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