Open Access
April 2012 Maximum likelihood estimation in log-linear models
Stephen E. Fienberg, Alessandro Rinaldo
Ann. Statist. 40(2): 996-1023 (April 2012). DOI: 10.1214/12-AOS986


We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table. We situate our results within the framework of extended exponential families, and we exploit the geometric properties of log-linear models. We propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log-linear model analysis.


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Stephen E. Fienberg. Alessandro Rinaldo. "Maximum likelihood estimation in log-linear models." Ann. Statist. 40 (2) 996 - 1023, April 2012.


Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62389
MathSciNet: MR2985941
Digital Object Identifier: 10.1214/12-AOS986

Primary: 62H17
Secondary: 62F99

Keywords: Extended exponential families , extended maximum likelihood estimators , log-linear models , Newton–Raphson algorithm , sampling zeros

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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