Consistent Estimation of Distribution Functions under Increasing Concave and Convex Stochastic Ordering

Estimation of Distribution Functions under Second Order Stochastic Dominance

The concept of stochastic ordering as introduced by Lehmann (1955) plays a major role in the theory and practice of statistics, and a large body of existing statistical work concerns itself with the problem of estimating distribution functions F and G under the constraint that F (x) ≤ G(x) for all x. Nevertheless in economic theory, the weaker concept of second order stochastic dominance plays ...

Multivariate Concave and Convex Stochastic Dominance

One of the big challenges in decision analysis is the assessment of a decision maker’s utility function. To the extent that the alternatives under consideration in a decision-making problem can be partially ordered based on less-than-full information about the utility function, the problem can be simplified somewhat by eliminating dominated alternatives. At the same time, partial orders can hel...

Convex and concave relaxations of implicit functions

Short Proofs of the Separation Theorems for L-convex/concave and M-convex/concave Functions

Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...

On convex-concave perception based functions

Perception based function (PBF) is given by the set of rules Ri:“If X is Ti then Y is Si”, where Ti is a linguistic term describing some fuzzy intervals Ai on the domain of real values of X and Si is a linguistic description of the shape of the function Y(X) on this interval. The methods of explicitation of such type of rules when Si are given by words QUICKLY INCREASING AND SLIGHTLY CONVEX, SL...