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Biometrika 1990 77(4):747-761; doi:10.1093/biomet/77.4.747
© 1990 by Biometrika Trust
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An approximation to maximum likelihood estimates in reduced models

D. R. COX and NANNY WERMUTH

Nuffield College Oxford OX1 1NF, U.K.
Psychologisches Institut, Johannes Gutenberg-Universität Mainz D-6500 Mainz, Federal Republic of Germany

An approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model, i.e. a model with additional parameters. The approximation is close provided that the data are consistent with the first model. Applications are described to log linear models for discrete data, to models for multivariate normal distributions with special covariance matrices and to mixed discrete-continuous models.

Key Words: Asymptotic theory • Concentration matrix • Conditional independence • Covariance matrix • Covariance selection • Generalized least squares • Graphical chain model • Information matrix • Log linear model


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