M-estimators and trimmed means: from Hilbert-valued to fuzzy set-valued data

Beatriz Sinova (), Stefan Van Aelst () and Pedro Terán ()
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Beatriz Sinova: University of Oviedo
Stefan Van Aelst: KU Leuven
Pedro Terán: University of Oviedo

Advances in Data Analysis and Classification, 2021, vol. 15, issue 2, No 2, 267-288

Abstract: Abstract Different approaches to robustly measure the location of data associated with a random experiment have been proposed in the literature, with the aim of avoiding the high sensitivity to outliers or data changes typical for the mean. In particular, M-estimators and trimmed means have been studied in general spaces, and can be used to handle Hilbert-valued data. Both alternatives are of interest due to their success in the classical framework. Since fuzzy set-valued data can be identified with a convex cone of a separable Hilbert space, the previous concepts have been recently applied to the one-dimensional fuzzy case. The aim of this paper is to extend M-estimators and trimmed means to p-dimensional fuzzy set-valued data, and to theoretically prove that they inherit robustness from the real settings. Some of such theoretical results are more general and directly apply to Hilbert-valued estimators and, in consequence, to functional data. A real-life example will also be included to illustrate the computation and behaviour of these estimators under contamination.

Keywords: Robust location; Finite sample breakdown point; Functional data; Random fuzzy sets; Random sets; 62G35; 62-07; 03E72 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11634-020-00402-x

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