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B0942
Title: A robust approach to summarize the location of functional data Authors:  Beatriz Sinova - University of Oviedo (Spain) [presenting]
Gil Gonzalez-Rodriguez - University of Oviedo (Spain)
Stefan Van Aelst - University of Leuven (Belgium)
Abstract: Some robust location measures to summarize the location of functional data have already been proposed in the literature, like, for instance, trimmed means (either involving depth functions or not). The aim is to extend another well-known and successful methodology used for univariate and multivariate real-valued data to the functional-valued setting, the so-called M-estimation. Such a generalization will be based on some developments from the literature for robust nonparametric density estimation. First, the theoretical results related to the existence and uniqueness of functional-valued M-estimators, as well as their consistency and robustness, will be established. The second part illustrates the computation of functional-valued M-estimators associated with some well-known choices for the loss function, such as Huber, Hampel and Tukey ones, and shows their finite-sample performance by means of several simulation studies.