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MAXIMUM LIKELIHOOD ESTIMATION IN LINEAR MODELS WITH EQUI‐CORRELATED RANDOM ERRORS
Author(s) -
Zhang Haimeng,
Rao M. Bhaskara
Publication year - 2006
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2006.00427.x
Subject(s) - mathematics , restricted maximum likelihood , maximum likelihood , maximum likelihood sequence estimation , estimator , statistics , linear model , quasi maximum likelihood , variance (accounting) , inference , random effects model , generalized linear model , multivariate statistics , estimation theory , likelihood function , computer science , artificial intelligence , medicine , meta analysis , accounting , business
Summary 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.