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

Aleksandra B. Slavkovic; Stephen E. Fienberg

doi:10.1007/978-3-540-25955-8_3

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

Aleksandra B. Slavkovic, Stephen E. Fienberg

Research output: Chapter in Book/Report/Conference proceeding › Chapter

12 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Josep Domingo-Ferrer, Vicenc Torra
Publisher	Springer Verlag
Pages	30-43
Number of pages	14
ISBN (Print)	3540221182, 9783540221180
DOIs	https://doi.org/10.1007/978-3-540-25955-8_3
State	Published - 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3050
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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10.1007/978-3-540-25955-8_3

Cite this

Slavkovic, A. B., & Fienberg, S. E. (2004). Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies. In J. Domingo-Ferrer, & V. Torra (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 30-43). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3050). Springer Verlag. https://doi.org/10.1007/978-3-540-25955-8_3

Slavkovic, Aleksandra B. ; Fienberg, Stephen E. / Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Josep Domingo-Ferrer ; Vicenc Torra. Springer Verlag, 2004. pp. 30-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Slavkovic, AB & Fienberg, SE 2004, Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies. in J Domingo-Ferrer & V Torra (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3050, Springer Verlag, pp. 30-43. https://doi.org/10.1007/978-3-540-25955-8_3

Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies. / Slavkovic, Aleksandra B.; Fienberg, Stephen E.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Josep Domingo-Ferrer; Vicenc Torra. Springer Verlag, 2004. p. 30-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3050).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies

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N2 - 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.

AB - 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.

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Slavkovic AB, Fienberg SE. Bounds for Cell Entries in Two-Way Tables Given Conditional Relative Frequencies. In Domingo-Ferrer J, Torra V, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 30-43. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-25955-8_3

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

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