OJS  Vol.4 No.3 , April 2014
Theoretical Properties of Composite Likelihoods
Abstract: 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.
Cite this paper: Wang, X. and Wu, Y. (2014) Theoretical Properties of Composite Likelihoods. Open Journal of Statistics, 4, 188-197. doi: 10.4236/ojs.2014.43018.

[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.