Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables
Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables
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 …