Maximum likelihood estimation in log-linear models
نویسندگان
چکیده
منابع مشابه
Maximum Likelihood Estimation in Log - Linear Models
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 non-existent MLE. Our conditions focus on the role of sampling zeros in the observed tabl...
متن کاملMaximum Likelihood Estimation in Log-Linear Models Supplementary Material: Algorithms
We use the theory developed in FR to derive efficient algorithms for extended maximum likelihood estimation in log-linear models under Poisson and product multinomial schemes. The restriction to these sampling schemes is motivated by a variety of reasons. First, these schemes encode sampling constraints that arise most frequently in practice. In particular, these are the sampling schemes practi...
متن کاملOn Maximum Likelihood Estimation in Log-Linear Models
In this article, we combine results from the theory of linear exponential families, polyhedral geometry and algebraic geometry to provide analytic and geometric characterizations of log-linear models and maximum likelihood estimation. Geometric and combinatorial conditions for the existence of the Maximum Likelihood Estimate (MLE) of the cell mean vector of a contingency table are given for gen...
متن کاملMaximum Likelihood Estimation in Log-Linear Models Supplementary Material
This document contains supplementary material to the article “Maximum Likelihood Estimation in LogLinear Models” by S.E. Fienberg and A. Rinaldo, henceforth referred to as FR. In section 2 we provide the proofs to some of the results announced in the article. Throughout, we assume familiarity with basic notions of polyhedral geometry: see Ziegler (1998), Schrijver (1998) and Rockafellar (1970) ...
متن کاملMaximum Likelihood Estimation in Log-linear
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...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2012
ISSN: 0090-5364
DOI: 10.1214/12-aos986