2017/08/09 by Caroline Uhler, Donald Richards, Uhler, Caroline +1
Computer Science · Decision Sciences · Mathematics · #05A20 #06D05 #62H17 (Primary) #62J12 (Secondary) #FOS: Mathematics #Graph theory and applications #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1708.02708
openalex publication_date 2017/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the lattice, \L, of all subsets of a multidimensional\ncontingency table and establish the properties of monotonicity and\nsupermodularity for the marginalization function, n(\⋅), on \L.\nWe derive from the supermodularity of n(\⋅) some generalized Fr 'echet\ninequalities complementing and extending inequalities of Dobra and Fienberg.\nFurther, we construct new monotonic and supermodular functions from n(\⋅),\nand we remark on the connection between supermodularity and some correlation\ninequalities for probability distributions on lattices. We also apply an\ninequality of Ky Fan to derive a new approach to Fr 'echet inequalities for\nmultidimensional contingency tables.\n