Estimating cell probabilities in contingency tables with constraints on marginals/conditionals by geometric programming with applications

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• 作者：Xinlei Wang (1)
  Johan Lim (2)
  Seung-Jean Kim (3)
  Kyu S. Hahn (4)
  
  1. Department of Statistical Science ; Southern Methodist University ; Dallas ; TX ; 75275 ; USA
  2. Department of Statistics ; Seoul National University ; Seoul ; Korea
  3. Citi Capital Advisors ; New York City ; NY ; USA
  4. Department of Communication ; Seoul National University ; Seoul ; Korea
  
• 关键词：Known marginals ; Ordered conditionals ; Ordered marginals ; Judgement post ; stratification ; Matlab ; Monomial ; Multinomial distribution ; Posynomial ; Stochastic ordering
• 刊名：Computational Statistics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：30
• 期：1
• 页码：107-129
• 全文大小：358 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Probability and Statistics in Computer Science
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1613-9658

文摘

Contingency tables are often used to display the multivariate frequency distribution of variables of interest. Under the common multinomial assumption, the first step of contingency table analysis is to estimate cell probabilities. It is well known that the unconstrained maximum likelihood estimator (MLE) is given by cell counts divided by the total number of observations. However, in the presence of (complex) constraints on the unknown cell probabilities or their functions, the MLE or other types of estimators may often have no closed form and have to be obtained numerically. In this paper, we focus on finding the MLE of cell probabilities in contingency tables under two common types of constraints: known marginals and ordered marginals/conditionals, and propose a novel approach based on geometric programming. We present two important applications that illustrate the usefulness of our approach via comparison with existing methods. Further, we show that our GP-based approach is flexible, readily implementable, effort-saving and can provide a unified framework for various types of constrained estimation of cell probabilities in contingency tables.