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Estimating the means and the covariances of fuzzy random variables


  • Shvedov, Alexey

    () (National Research University Higher School of Economics, Moscow, Russian Federation)


At present, methods of fuzzy mathematics are applied in different fields. For example, fuzzy numbers can be used to model returns of assets in portfolio selection problem when historical data is unavailable. While for other assets possibility of using random variables should be kept. This paper presents new estimators of the means and the covariances of fuzzy random variables. Unbiasedness and consistency of these estimators are established.

Suggested Citation

  • Shvedov, Alexey, 2016. "Estimating the means and the covariances of fuzzy random variables," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 42, pages 121-138.
  • Handle: RePEc:ris:apltrx:0294

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    References listed on IDEAS

    1. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.
    2. Fang, Yong & Lai, K.K. & Wang, Shou-Yang, 2006. "Portfolio rebalancing model with transaction costs based on fuzzy decision theory," European Journal of Operational Research, Elsevier, vol. 175(2), pages 879-893, December.
    3. Huang, Xiaoxia, 2007. "Two new models for portfolio selection with stochastic returns taking fuzzy information," European Journal of Operational Research, Elsevier, vol. 180(1), pages 396-405, July.
    4. Dabuxilatu Wang, 2004. "A note on consistency and unbiasedness of point estimation with fuzzy data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 93-104, July.
    5. K. Thiagarajah & A. Thavaneswaran, 2006. "Fuzzy random-coefficient volatility models with financial applications," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 503-524, November.
    6. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    7. Liu, Fan-Yong, 2009. "Pricing currency options based on fuzzy techniques," European Journal of Operational Research, Elsevier, vol. 193(2), pages 530-540, March.
    8. Wu, Hsien-Chung, 2003. "The fuzzy estimators of fuzzy parameters based on fuzzy random variables," European Journal of Operational Research, Elsevier, vol. 146(1), pages 101-114, April.
    9. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
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    More about this item


    fuzzy data analysis; fuzzy random variables; point estimation; unbiasedness; consistency;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General


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