Theoretical Properties of Composite Likelihoods


The general functional form of composite likelihoods is derived by minimizing the Kullback-Leibler distance under structural constraints associated with low dimensional densities. Connections with the I-projection and the maximum entropy distributions are shown. Asymptotic properties of composite likelihood inference under the proposed information-theoretical framework are established.

Share and Cite:

Wang, X. and Wu, Y. (2014) Theoretical Properties of Composite Likelihoods. Open Journal of Statistics, 4, 188-197. doi: 10.4236/ojs.2014.43018.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Lindsay, B. (1988) Composite Likelihood Methods. Contemporary Mathematics, 80, 221-239.
[2] Varin, C., Reid, N. and Firth, D. (2011) An Overview of Composite Likelihood Methods. Statistica Sinica, 21, 5-42.
[3] Cox, D. and Reid, N. (2011) An Note on Pseudo-Likelihood Constructed from Marginal Densities. Biometrika, 91, 729-737.
[4] Mollenberghs, G. and Verbeke, G. (2005) Models for Discrete Longitudinal Data. Springer, Inc., New York.
[5] Mardia, K.V., Kent, J.T., Hughes, G. and Taylor, C.C. (2009) Maximum Likelihood Estimation Using Composite Likelihoods for Closed Exponential Families. Biometrika, 96, 975-982.
[6] Gao, X. and Song, P.X. (2010) Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data. Journal of the American Statistical Association, 105, 1531-1540.
[7] Cover, T.M. and Thomas, J.A. (2006) Elements of Information Theory. John Wiley & Sons, Inc., Hoboken.
[8] Kullback, S. (1959) Information Theory and Statistics. Dove Publications, Inc., New York.
[9] Csiszár, I. (1975) I-Divergence Geometry of Probability Distributions as Minimization Problems. Annals of Probability, 3, 146-158.
[10] Wald, A. (1949) Note on the Consistency of the Maximum Likelihood Estimate. Annals of Mathematical Statistics, 20, 595.
[11] Wolfowitz, J. (1949) On Wald’s Proof of the Consistency of the Maximum Likelihood Estimate. Annals of Mathematical Statistics, 20, 601-602.
[12] Shao, J. (2003) Mathematical Statistics. 2nd Edition, Springer, Inc., New York.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.