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Estimating the means and the covariances of fuzzy random variables

Author

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  • Shvedov, Alexey

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

Abstract

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, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 121-138.
    • Handle: RePEc:ris:apltrx:0294
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    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    9. Liu, Fan-Yong, 2009. "Pricing currency options based on fuzzy techniques," European Journal of Operational Research, Elsevier, vol. 193(2), pages 530-540, March.
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    Cited by:

    1. Brychykova, A., 2019. "Capital Asset Pricing Model Using Fuzzy Data and Application for the Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 43(3), pages 58-77.

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    More about this item

    Keywords

    fuzzy data analysis; fuzzy random variables; point estimation; unbiasedness; consistency;
    All these keywords.

    JEL classification:

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

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