Unconstrained parametrizations for variance-covariance matrices View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1996-09

AUTHORS

José C. Pinheiro, Douglas M. Bates

ABSTRACT

The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We compare the parametrizations based on their computational efficiency and statistical interpretability. The results described here are particularly useful in maximum likelihood and restricted maximum likelihood estimation in linear and non-linear mixed-effects models, but are also applicable to other areas of statistics. More... »

PAGES

289-296

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00140873

DOI

http://dx.doi.org/10.1007/bf00140873

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1039962386


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