Mathematics – Statistics Theory
Scientific paper
2006-03-21
Computational Statistics and Data Analysis, Vol. 53, 966-978. (2009)
Mathematics
Statistics Theory
Scientific paper
10.1016/j.csda.2008.11.013
We propose iterative proportional scaling (IPS) via decomposable submodels for maximizing likelihood function of a hierarchical model for contingency tables. In ordinary IPS the proportional scaling is performed by cycling through the elements of the generating class of a hierarchical model. We propose to adjust more marginals at each step. This is accomplished by expressing the generating class as a union of decomposable submodels and cycling through the decomposable models. We prove convergence of our proposed procedure, if the amount of scaling is adjusted properly at each step. We also analyze the proposed algorithms around the maximum likelihood estimate (MLE) in detail. Faster convergence of our proposed procedure is illustrated by numerical examples.
Endo Yushi
Takemura Akimichi
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