Abstract #301116

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JSM 2003 Abstract #301116
Activity Number: 21
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Survey Research Methods
Abstract - #301116
Title: Bounds for Cell Entries in Contingency Tables Given Arbitrary Sets of Conditional and Marginal Distributions
Author(s): Aleksandra B. Slavkovic*+
Companies: Carnegie Mellon University
Address: Department of Statistics, Pittsburgh, PA, 15213,
Keywords: bounds ; DAGs ; contingency table ; conditional specification ; geometry ; disclosure limitation
Abstract:

In recent work on statistical methods for confidentiality and disclosure limitation, Dobra and Fienberg (2000) have generalized Bonferroni-Frechet-Hoeffding bounds for cell entries in k-way contingency tables given marginal totals and decomposable graphs. We develop upper and lower bounds for cell entries given arbitrary sets of marginals and conditionals. We give a complete characterization of the two-way table problem and discuss extensions to multiway tables, including relationships to directed acyclic graphical models. We also employ a geometric approach to describe the locus of all possible tables under the given constraints. We consider the case of 2x2 contingency tables in detail.

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