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Biometrika 1998 85(4):973-979; doi:10.1093/biomet/85.4.973
© 1998 by Biometrika Trust
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MISCELLANEA

Information matrix computation from conditional information via normal approximation

CHUANHAI LIU

Bell Laboratories, Lucent Technologies Murray Hill, New Jersey 07974, U.S.A.liu{at}research.bell-labs.com

This paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters. Philosophically, the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference. Technically, the method makes use of two facts: the information for a one-dimensional parameter can be well computed when the loglikelihood is approximately quadratic over the range corresponding to a small positive confidence interval; and the covariance matrix of a normal distribution can be obtained from its one-dimensional conditional distributions whose sample spaces span the sample space of the joint distribution. We illustrate the method with its application to a linear mixed-effects model.

Key Words: Conditional information • EM algorithm • Fisher information • Maximum likelihood • Q–Q plot • SEM algorithm


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