Fréchet and Bonferroni Bounds for
Multi-way Tables of Counts With Applications to Disclosure Limitation

Stephen E. Fienberg


Upper and lower bounds on cell counts in cross-classifications of positive counts play important roles in a number of the disclosure limitation procedures, e.g., cell suppression and data swapping. Some features of the Fréchet bounds are well-known, intuitive, and are regularly used by those working on disclosure limitation methods, especially those for two-dimensional tables. The multivariate versions of these bounds and other related bounds such as those calculated using the Bonferroni approach are more complex, however, but they have potentially great import for current disclosure limitation methodology. The purpose of this paper is to describe the key results on this topic.

Keywords: Contingency tables; Copulas; Loglinear models; Marginal bounds.

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