Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies
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.
KeywordsConfidentiality Contingency tables Integer programming Linear programming Markov bases Statistical disclosure control Tabular data
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