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On Modification of the Law of Large Numbers and Linear Regression of Fuzzy Random Variables

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Recent Developments in Stochastic Methods and Applications (ICSM-5 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 371))

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Abstract

Extreme properties of the average characteristics of fuzzy random variables are given. A new form of the law of large numbers for fuzzy random variables is established. An optimal linear regression of fuzzy random variables is constructed, in which the coefficients are similar to the Fourier coefficients. It is shown that under certain conditions, the optimal regression has the maximum cosine of the angle with the predicted fuzzy random variable.

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Author information

Authors and Affiliations

  1. Air Force Academy named after N.E. Zhukovsky and Y.U. Gagarin, Voronezh, Russian Federation

    Vladimir L. Khatskevich

Authors
  1. Vladimir L. Khatskevich
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Editors and Affiliations

  1. Steklov Mathematical Institute of RAS, Moscow, Russia

    Albert N. Shiryaev

  2. Applied Probability & Informatics, Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. Applied Probability & Informatics, Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Dmitry V. Kozyrev

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Khatskevich, V.L. (2021). On Modification of the Law of Large Numbers and Linear Regression of Fuzzy Random Variables. In: Shiryaev, A.N., Samouylov, K.E., Kozyrev, D.V. (eds) Recent Developments in Stochastic Methods and Applications. ICSM-5 2020. Springer Proceedings in Mathematics & Statistics, vol 371. Springer, Cham. https://doi.org/10.1007/978-3-030-83266-7_6

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