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Biometrika 2004 91(3):729-737; doi:10.1093/biomet/91.3.729
© 2004 by Biometrika Trust
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A note on pseudolikelihood constructed from marginal densities

D. R. Cox1 and N. Reid2

1 Nuffield College, Oxford, OX1 1NF, U.K. david.cox{at}nuf.ox.ac.uk, 2 Department of Statistics, University of Toronto, Toronto M5S 3GS, Canada reid{at}utstat.utoronto.ca

For likelihood-based inference involving distributions in which high-dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single qx1 vector of observations is observed are examined. Conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied. Some examples are analysed in detail.

Key Words: Component of variance; Composite likelihood; Consistency of estimation; Dichotomised Gaussian distribution; Generalised estimating equation; Genetic statistics; Maximum likelihood; Pseudolikelihood

Received August 2003. Revised January 2004.


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