The Annals of Statistics

Maximum likelihood estimation in log-linear models

Stephen E. Fienberg and Alessandro Rinaldo

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Abstract

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.

Article information

Source
Ann. Statist. Volume 40, Number 2 (2012), 996-1023.

Dates
First available in Project Euclid: 18 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1342625459

Digital Object Identifier
doi:10.1214/12-AOS986

Mathematical Reviews number (MathSciNet)
MR2985941

Zentralblatt MATH identifier
1274.62389

Subjects
Primary: 62H17: Contingency tables
Secondary: 62F99: None of the above, but in this section

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

Citation

Fienberg, Stephen E.; Rinaldo, Alessandro. Maximum likelihood estimation in log-linear models. Ann. Statist. 40 (2012), no. 2, 996--1023. doi:10.1214/12-AOS986. https://projecteuclid.org/euclid.aos/1342625459.


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