Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from e...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1977-06, Vol.72 (358), p.320-338
Main Author: Harville, David A.
Format: Article
Language:English
Subjects:
Analytical estimating
Biometrics
Estimation methods
Estimators
Mathematical vectors
Maximum likelihood
Maximum likelihood computations
Maximum likelihood estimation
Maximum likelihood estimators
Mixed linear models
Restricted maximum likelihood
Statistical variance
Theory and Methods
Unbiased estimators
Variance component estimation
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Summary:Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1977.10480998