Title: Combining nonparametric functionals for more effective decision-making and inference Authors:  Arne Bathke - University of Salzburg (Austria) [presenting]
Abstract: Nonparametric statistical methods are usually characterized by rather generous invariance properties, as well as robustness against departures from narrow model classes. This has made them very popular in the last decades, and the attractiveness of nonparametric methods transfers to many data science applications where specific parametric models are not justifiable. However, a shortcoming of those inference procedures that rely on the nonparametric relative effect (Mann-Whitney functional) as their base functional is their inability to capture differences between distributions that cannot be described by a stochastic tendency. To this end, we have introduced a functional describing distributional overlap and derived a consistent estimator along with its asymptotic distribution, even jointly with that of the relative effect estimator. Combining these two functionals allows for much more versatile inference, which we will demonstrate in this presentation. Also, we will try to address the issue of interpretability of the resulting effect measures, as straightforward interpretability is key to their usability in practice.