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

Author

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  • Victor De Oliveira

    (The 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.

Suggested Citation

  • Victor De Oliveira, 2010. "Maximum Lilkelihood and Restricted Maximum Likelihood Estimation for a Class of Gaussian Markov Random Fields," Working Papers 0110, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0136mss
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    More about this item

    Keywords

    Eigenvalues and eigenvectors; Profile likelihood; Restricted likelihood; Spatial data.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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