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Coordinate-Free Exponential Families on Contingency Tables

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dc.contributor.advisor Rudas, Tamas en_US Klimova, Anna en_US 2012-09-13T17:40:41Z 2012-09-13T17:40:41Z 2012-09-13 2012 en_US
dc.identifier.other Klimova_washington_0250E_10253.pdf en_US
dc.description Thesis (Ph.D.)--University of Washington, 2012 en_US
dc.description.abstract We propose a class of coordinate-free multiplicative models on the set of positive distributions on contingency tables and on some sets of cells of a more general structure. The models are called relational and are generated by subsets of cells, some of which may not be induced by marginals of the table, and, under the model, every cell parameter is the product of effects associated with subsets the cell belongs to. Such models are useful in analyzing incomplete tables and generalized independence structures not pertaining to subsets of variables forming the table. We reveal when a relational model is regular or else a curved exponential family. We establish necessary and sufficient conditions for the existence and uniqueness of the MLE in the curved case. We also determine the conditions under which the properties of the MLE under relational models are comparable to those under hierarchical log-linear models and prove a generalization of Birch's theorem. We propose a generalization of the iterative proportional fitting procedure that can be used for maximum likelihood estimation under relational models and prove its convergence. Finally, we use the relational model framework to contribute to the ongoing debate whether British social mobility is declining and compare the patterns of occupational mobility in Great Britain in 1991 and 2005. en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.rights Copyright is held by the individual authors. en_US
dc.subject en_US
dc.subject.other Statistics en_US
dc.subject.other Statistics en_US
dc.title Coordinate-Free Exponential Families on Contingency Tables en_US
dc.type Thesis en_US
dc.embargo.terms No embargo en_US

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