Klimova, AnnaIST Austria; Rudas, Tamás
The paper describes a generalized iterative proportional fitting procedure that 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 that 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. An implementation of the algorithm is available as an R-package.
Scandinavian Journal of Statistics
Part of the material presented here was contained in the PhD thesis of the first author to which the second author and Thomas Richardson were advisers. The authors wish to thank him for several comments and suggestions. We also thank the reviewers and the Associate Editor for helpful comments. The proof of Proposition 1 uses the idea of Olga Klimova, to whom the authors are also indebted. The second author was supported in part by Grant K-106154 from the Hungarian National Scientific Research Fund (OTKA).
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Klimova A, Rudas T. Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. 2015;42(3):832-847. doi:10.1111/sjos.12139
Klimova, A., & Rudas, T. (2015). Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. Wiley. https://doi.org/10.1111/sjos.12139
Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.” Scandinavian Journal of Statistics. Wiley, 2015. https://doi.org/10.1111/sjos.12139.
A. Klimova and T. Rudas, “Iterative scaling in curved exponential families,” Scandinavian Journal of Statistics, vol. 42, no. 3. Wiley, pp. 832–847, 2015.
Klimova A, Rudas T. 2015. Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. 42(3), 832–847.
Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.” Scandinavian Journal of Statistics, vol. 42, no. 3, Wiley, 2015, pp. 832–47, doi:10.1111/sjos.12139.