dissimilarity measures based on trimmings
Eustasio Del Barrio
Universidad de Valladolid, Spain
The talk introduces an analysis of similarity of distributions based on
measuring some distance between trimmed distributions. Our main
innovation is the use of the impartial trimming methodology, already
considered in robust statistics, which we adapt to the setup of model
checking. By considering trimmed probability measures we introduce a
way to test whether the core of the random generator underlying the
data fits a given pattern.
Instead of simply removing mass at non-central zones for providing some
robustness to the similarity analysis, we develop a data-driven
trimming method aimed at maximizing similarity between distributions.
Dissimilarity is then measured in terms of the distance between the
optimally trimmed distributions. Our main choice for applications is
the Wasserstein metric, but other distances might be of interest for
different applications.We provide illustrative examples showing the
improvements over previous
approaches and give the relevant asymptotic results to justify the use
of this methodology in applications.