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

Article type: Research Article

Authors: Dobra, Adrian^a | Fienberg, Stephen E.^b

Affiliations: [a] Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. Tel.: +1 412 268 7829; Fax: +1 412 268 7828; E-mail: [email protected] | [b] Department of Statistics and Center for Automated Learning and Discovery, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. Tel.: +1 412 268 2723; Fax: +1 412 268 7828; E-mail: [email protected]

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.

Keywords: statistical disclosure control, log-linear models, decomposable models, reducible models, integer programming

DOI: 10.3233/SJU-2001-18411

Journal: Statistical Journal of the United Nations Economic Commission for Europe, vol. 18, no. 4, pp. 363-371, 2001