Bounds for cell entries in contingency tables induced by fixed marginal totals with applications to disclosure limitation

Abstract

We describe new results for upper and lower bounds on the entries in multi-way tables of counts based on a set of released and possibly overlapping marginal tables which have practical importance for assessing disclosure risk. In particular, we present a generalized version of the shuttle algorithm proposed by Buzzigoli and Giusti that is proven to compute sharp integer bounds for an arbitrary set of fixed marginals. The method forms part of a project developing a Web-based query system for statistical databases. Its goal is to allow the use of disclosure limitation methods in response to a series of queries in which the public knowledge of releases is cumulative.