On the closure of relational models

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• 作者：Anna Klimova^a ; ^{aklimova25@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Tamá ; s Rudas^b ; ^{rudas@tarki.hu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62H12 ; 62H17
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：143
• 期：Complete
• 页码：440-452
• 全文大小：463 K

文摘

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this generality, the MLEs under Poisson and multinomial sampling are not always identical. This paper deals with the theory of maximum likelihood estimation in the case when there are observed zeros in the data. A unique MLE to such data is shown to always exist in the set of pointwise limits of sequences of distributions in the original model. This set is equal to the closure of the original model with respect to the Bregman information divergence. The same variant of iterative scaling may be used to compute the MLE whether it is in the original model or in its closure.