Maximum likelihood estimation in log-linear models
Stephen E. Fienberg, Alessandro Rinaldo
The Annals of Statistics · 2012 · Volume 40 · Issue 2
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.
Keywords
62F99, 62H17, Extended exponential families, extended maximum likelihood estimators, log-linear models, Newton–Raphson algorithm, sampling zeros
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