2013/07/11 by Anna Klimová, Anna Klimova, Klimova, Anna +3
Mathematics · Physics and Astronomy · #62J12 #Advanced Statistical Methods and Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Mechanics and Entropy #Statistical Methods and Bayesian Inference #msc:62J12 #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.1307.3282
The paper has one figure
openalex publication_date 2013/07/11 · arxiv created 2014/03/29 · arxiv updated 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper describes a generalized iterative proportional fitting procedure which can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to multivariate discrete sample spaces which do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling and Improved Iterative Scaling, fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by-product, estimates of the multiplicative parameters are also obtained.