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Advances in Data Analysis and Classification

, Volume 11, Issue 4, pp 731–758 | Cite as

Robust scale estimators for fuzzy data

  • Sara de la Rosa de Sáa
  • María Asunción Lubiano
  • Beatriz Sinova
  • Peter Filzmoser
Regular Article

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.

Keywords

Finite sample breakdown point Empirical bias curves  Fuzzy numbers Random fuzzy numbers Robustness Scale estimation Sensitivity curves 

Mathematics Subject Classification

62F35 62A86 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sara de la Rosa de Sáa
    • 1
    • 2
  • María Asunción Lubiano
    • 1
  • Beatriz Sinova
    • 1
  • Peter Filzmoser
    • 2
  1. 1.Departamento de Estadística e I.O. y D.M.Universidad de OviedoOviedoSpain
  2. 2.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

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