Seminario della prof.ssa Ana Colubi (Università di Oviedo, Spagna).
Abstract
Numerous experimental studies involve semi-quantitative expert information, or measured in a non-precise way, which can be modeled with interval (fluctuations, grouped data, etc.) or fuzzy (ratings, opinions, perceptions etc.) data. A general framework to analyze these kinds of inexact data with statistical tools developed for Hilbertian random variables will be presented. Robust estimation in Hilbert spaces is specially relevant for its applications in the treatment of contaminated functional data. Specifically, the trimmed mean was already defined and analyzed under ideal conditions. However its estimation has not been efficiently implemented. An algorithm to compute the sample trimmed mean in Hilbert spaces is presented and its robust properties are briefly discussed. To show the performance of the algorithm some case studies concerning functional and fuzzy data will be presented.