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Biometrika Advance Access originally published online on October 29, 2009
Biometrika 2009 96(4):975-982; doi:10.1093/biomet/asp056
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© 2009 Biometrika Trust

Miscellanea

Maximum likelihood estimation using composite likelihoods for closed exponential families

Kanti V. Mardia and John T. Kent

Department of Statistics, University of Leeds, Leeds, LS2 9JT, U.K. k.v.mardia{at}leeds.ac.uk j.t.kent{at}leeds.ac.uk

Gareth Hughes

Novartis International AG, CH-4002 Basel, Switzerland ghughes{at}live.co.uk

Charles C. Taylor

Department of Statistics, University of Leeds, Leeds, LS2 9JT, U.K. c.c.taylor{at}leeds.ac.uk

Received for publication 1 April 2008. Revision received 1 May 2009.
  Abstract

In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases the parameter estimate obtained by maximizing a composite likelihood can be viewed as an approximation to the full maximum likelihood estimate. An application is given to an example in directional data based on a bivariate von Mises distribution.

Key Words: Bivariate von Mises distribution • Closed exponential family • Fisher information • Log-linear model • Maximum likelihood • Multivariate normal distribution • Pseudolikelihood


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