Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies

  • Aleksandra B. Slavkovic
  • Stephen E. Fienberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3050)


In recent work on statistical methods for confidentiality and disclosure limitation, Dobra and Fienberg (2000, 2003) and Dobra (2002) have generalized Bonferroni-Fréchet-Hoeffding bounds for cell entries in k-way contingency tables given marginal totals. In this paper, we consider extensions of their approach focused on 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 some implications to statistical disclosure limitation. In particular, we employ tools from computational algebra to describe the locus of all possible tables under the given constraints and discuss how this additional knowledge affects the disclosure.


Confidentiality Contingency tables Integer programming Linear programming Markov bases Statistical disclosure control Tabular data 


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Aleksandra B. Slavkovic
    • 1
  • Stephen E. Fienberg
    • 2
  1. 1.Department of StatisticsCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Statistics, Center for Automated Learning and Discovery, Center for Computer Communications and SecurityCarnegie Mellon UniversityPittsburghUSA

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