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Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-01-13
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood.
In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically.
Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established.
As a consequence, the main result is obtained: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices.
The implication of this theorem on Kriging hyperparameter optimization is exposed.
A nonartificial example is presented, where maximum likelihood-based Kriging model training is necessarily bound to fail.
American Psychological Association (APA)
Zimmermann, Ralf. 2011. Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes. Journal of Applied Mathematics،Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-476124
Modern Language Association (MLA)
Zimmermann, Ralf. Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes. Journal of Applied Mathematics No. 2010 (2010), pp.1-17.
https://search.emarefa.net/detail/BIM-476124
American Medical Association (AMA)
Zimmermann, Ralf. Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes. Journal of Applied Mathematics. 2011. Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-476124
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476124