Maximum Lilkelihood and Restricted Maximum Likelihood Estimation for a Class of Gaussian Markov Random Fields

Victor De Oliveira
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Victor De Oliveira: The University of Texas at San Antonio

No 110, Working Papers from College of Business, University of Texas at San Antonio

Abstract: This work describes a Gaussian Markov random field model that includes several previously proposed models, and studies properties of their maximum likelihood (ML) and restricted maximum likelihood (REML) estimators in a special case. Specifically, for models where a particular relation holds between the regression and precision matrices of the model, we provide sufficient conditions for existence and uniqueness of ML and REML estimators of the covariance parameters, and provide a straightforward way to compute them. It is found that the ML estimator always exists while the REML estimator may not exist with positive probability. A numerical comparison suggests that for this model ML estimators of covariance parameters have, overall, better frequentist properties than REML estimators.

Keywords: Eigenvalues and eigenvectors; Profile likelihood; Restricted likelihood; Spatial data. (search for similar items in EconPapers)
JEL-codes: C11 C31 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2010-08-16
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