Maximum Likelihood Estimation in Linear Models with Equi-Correlated Random Errors

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Haimeng Zhang, Associate Professor (Creator)
The University of North Carolina at Greensboro (UNCG )
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Abstract: Necessary and sufficient conditions for the existence of maximum likelihood estimators of unknown parameters in linear models with equi-correlated random errors are presented. The basic technique we use is that these models are, first, orthogonally transformed into linear models with two variances, and then the maximum likelihood estimation problem is solved in the environment of transformed models. Our results generalize a result of Arnold, S. F. (1981)[The theory of linear models and multivariate analysis. Wiley, New York]. In addition, we give necessary and sufficient conditions for the existence of restricted maximum likelihood estimators of the parameters. The results of Birkes, D. & Wulff, S. (2003)[Existence of maximum likelihood estimates in normal variance-components models. J Statist Plann. Inference.113, 35–47] are compared with our results and differences are pointed out.

Additional Information

Australian and New Zealand Journal of Statistics, 48(1), 79 – 93
Language: English
Date: 2006
equi-correlated variables, linear models, maximum likelihood estimator, multivariate normal distribution, restricted maximum likelihood estimator

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