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

Author

Listed:
  • Beatriz Sinova

    (University of Oviedo)

  • Stefan Van Aelst

    (KU Leuven)

  • Pedro Terán

    (University of Oviedo)

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.

Suggested Citation

  • Beatriz Sinova & Stefan Van Aelst & Pedro Terán, 2021. "M-estimators and trimmed means: from Hilbert-valued to fuzzy set-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 267-288, June.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:2:d:10.1007_s11634-020-00402-x
    DOI: 10.1007/s11634-020-00402-x
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    References listed on IDEAS

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