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Robust scale estimators for fuzzy data

Author

Listed:
  • Sara de la Rosa de Sáa

    (Universidad de Oviedo
    Vienna University of Technology)

  • María Asunción Lubiano

    (Universidad de Oviedo)

  • Beatriz Sinova

    (Universidad de Oviedo)

  • Peter Filzmoser

    (Vienna University of Technology)

Abstract

Observations distant from the majority or deviating from the general pattern often appear in datasets. Classical estimates such as the sample mean or the sample variance can be substantially affected by these observations (outliers). Even a single outlier can have huge distorting influence. However, when one deals with real-valued data there exist robust measures/estimates of location and scale (dispersion) which reduce the influence of these atypical values and provide approximately the same results as the classical estimates applied to the typical data without outliers. In real-life, data to be analyzed and interpreted are not always precisely defined and they cannot be properly expressed by using a numerical scale of measurement. Frequently, some of these imprecise data could be suitably described and modelled by considering a fuzzy rating scale of measurement. In this paper, several well-known scale (dispersion) estimators in the real-valued case are extended for random fuzzy numbers (i.e., random mechanisms generating fuzzy-valued data), and some of their properties as estimators for dispersion are examined. Furthermore, their robust behaviour is analyzed using two powerful tools, namely, the finite sample breakdown point and the sensitivity curves. Simulations, including empirical bias curves, are performed to complete the study.

Suggested Citation

  • Sara de la Rosa de Sáa & María Asunción Lubiano & Beatriz Sinova & Peter Filzmoser, 2017. "Robust scale estimators for fuzzy 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. 11(4), pages 731-758, December.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:4:d:10.1007_s11634-015-0210-1
    DOI: 10.1007/s11634-015-0210-1
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    References listed on IDEAS

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    1. Ramos-Guajardo, Ana Belén & Lubiano, María Asunción, 2012. "K-sample tests for equality of variances of random fuzzy sets," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 956-966.
    2. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
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    Cited by:

    1. 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.

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