M-estimators and trimmed means: from Hilbert-valued to fuzzy set-valued data. (English) Zbl 07363874
Summary: 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.
MSC:
| 62G35 | Nonparametric robustness |
| 62-07 | Data analysis (statistics) (MSC2010) |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
robust location; finite sample breakdown point; functional data; random fuzzy sets; random setsReferences:
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