Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables
Name
10.1.pdf
Description
Published version
Size
373.4 KB
Format
Adobe PDF
Checksum (MD5)
f26be11bdaba3a528ac5d41f43ce8bc1
Author(s)
Uhler, Caroline
Richards, Donald
Date Issued
2019
Journal
Journal of Algebraic Statistics
Publisher
Paul V. Galvin Library/Illinois Institute of Technology
Version
Final published version
Abstract
We consider the lattice, $\mathcal{L}$, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, $n(\cdot)$, on $\mathcal{L}$. We derive from the supermodularity of $n(\cdot)$ some generalized Fr\'echet inequalities complementing and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from $n(\cdot)$, and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequality of Ky Fan to derive a new approach to Fr\'echet inequalities for multidimensional contingency tables.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Terms of Use
Creative Commons Attribution NonCommercial License 4.0
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DOI of Published Version
https://doi.org/10.18409/JAS.V10I1.71
