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Robust scale estimators for fuzzy data

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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.

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Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, 33007, Oviedo, Spain

    Sara de la Rosa de Sáa, María Asunción Lubiano & Beatriz Sinova

  2. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, 1040, Vienna, Austria

    Sara de la Rosa de Sáa & Peter Filzmoser

Authors
  1. Sara de la Rosa de Sáa
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  2. María Asunción Lubiano
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  3. Beatriz Sinova
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  4. Peter Filzmoser
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Corresponding author

Correspondence to María Asunción Lubiano.

Additional information

Authors are very grateful for the insight comments from the reviewers of the original. The research in this paper has been partially supported by/benefited from Principality of Asturias Grants GRUPIN14-101, Research Contract E-33-2015-0040746 (this one for Sinova) and Severo Ochoa BP12012 (this one for De la Rosa de Sáa), and the Spanish Ministry of Economy and Competitiveness Grant MTM2013-44212-P. Their financial support is gratefully acknowledged.

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de la Rosa de Sáa, S., Lubiano, M.A., Sinova, B. et al. Robust scale estimators for fuzzy data. Adv Data Anal Classif 11, 731–758 (2017). https://doi.org/10.1007/s11634-015-0210-1

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  • DOI: https://doi.org/10.1007/s11634-015-0210-1

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