María Concepción López-Díaz

Ranking Star-Shaped Valued Mappings with Respect to Shape Variability

The study of shapes is a difficult topic, but it is becoming more and more important as computer vision techniques are already crucial in many research fields. Concretely, the variability of shapes is the basis for many criteria of symptom definition in medical diagnosis. This article introduces a stochastic order to address the variability of star-shaped sets. The main properties of the order are analyzed. An example of an application to hypothesis testing in medical diagnosis is also provided. Namely, we study if there are significant differences between healthy and diseased corneal endothelia with respect to cell shapes by means of ocular images.

A stochastic comparison of customer classifiers with an application to customer attrition in commercial banking

The classification of clients is an essential matter in commercial banking, insurance companies, electrical corporations, communication business, etc. Those companies frequently classify their customers by means of the information provided by the so-called classifier. Motivated by the need to compare systems of classification, we introduce a new stochastic order which permits the comparison of classifiers. The stochastic order is analysed in detail, providing characterizations and properties as well as connections with other stochastic orders and other classification systems. Such an order is applied to compare some classifiers used by a Spanish commercial banking to analyse the key problem of customer churn, obtaining conclusive results by means of real databases. Namely, the optimal classifier among them in the new stochastic order is obtained.

When is an integral stochastic order generated by a poset

Given a partial order ⪯ on a set X, one can consider the class of ⪯-preserving real functions on X characterized by x⪯y implies f(x)≤f(y). Such a class of functions allows us the generation of a binary relation ⪯g on the set of probabilities associated with X by means of P⪯gQ when ∫fdP≤∫fdQ for all ⪯-preserving functions f. In this paper we characterize when for an integral stochastic order ⪯˜ on the set of probabilities associated with X, there exists a partial order ⪯ on X such that the relation ⪯g generated by the class of ⪯-preserving functions is equal to ⪯˜. The above characterization is related to the maximal generator of ⪯˜, a result which can be applied for the search of maximal generators of stochastic orders generated by posets.MSC:06A06, 60E15.

Some Comments on Stochastic Orders and Posets

In this paper, we review some relations between partially ordered sets and stochastic orders. We focus our attention on analyzing if the property of being order-isomorphic is transferred from partially ordered sets to the stochastic orders generated by such partially ordered sets.

On the Preservations of Contractions: An Application to Stochastic Orders

We obtain conditions for a function to preserve contractions, which do not involve convex sums of orthogonal matrices. The verification of such conditions implies, in general, a considerable saving of time compared with checking conditions already known. An application to stochastic orders of the above results is developed.