Maximum likelihood estimation in log-linear models

@article{Fienberg2012MaximumLE,
  title={Maximum likelihood estimation in log-linear models},
  author={Stephen E. Fienberg and Alessandro Rinaldo},
  journal={Annals of Statistics},
  year={2012},
  volume={40},
  pages={996-1023}
}
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… Expand

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