On the closure of relational models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:143

Article

Klimova, Anna¹  Rudas, Tamas² 

[1] IST Austria, A-3400 Klosterneuburg, Austria

[2] Eotvos Lorand Univ, H-1117 Budapest, Hungary

关键词: Algebraic variety;    Bregman divergence;    Contingency table;    Extended MLE;    Iterative scaling;    Relational model;   

DOI  :  10.1016/j.jmva.2015.10.005

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free