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Scale and shape mixtures of matrix variate extended skew normal distributions

Author

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  • Rezaei, Amir
  • Yousefzadeh, Fatemeh
  • Arellano-Valle, Reinaldo B.

Abstract

In this paper, we propose a matrix extension of the scale and shape mixtures of multivariate skew normal distributions and present some particular cases of this new class. We also present several formal properties of this class, such as the marginal distributions, the moment generating function, the distribution of linear and quadratic forms, and the selection and stochastic representations. In addition, we introduce the matrix variate tail conditional expectation measure and derive this risk measure for the scale and shape mixtures of matrix variate extended skew normal distributions. We present an efficient EM-type algorithm for the computation of maximum likelihood estimates of parameters in some special cases of the proposed class. Finally, we conduct a small simulation study and fit various special cases of the new class to a real dataset.

Suggested Citation

  • Rezaei, Amir & Yousefzadeh, Fatemeh & Arellano-Valle, Reinaldo B., 2020. "Scale and shape mixtures of matrix variate extended skew normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x2030230x
    DOI: 10.1016/j.jmva.2020.104649
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    References listed on IDEAS

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    1. Gallaugher, Michael P.B. & McNicholas, Paul D., 2019. "Three skewed matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 103-109.
    2. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    3. Shimin Zheng & Jeff Knisley & Kesheng Wang, 2016. "Moments and quadratic forms of matrix variate skew normal distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 794-803, February.
    4. Rappoport, Peter & White, Eugene N., 1993. "Was There a Bubble in the 1929 Stock Market?," The Journal of Economic History, Cambridge University Press, vol. 53(3), pages 549-574, September.
    5. Arellano-Valle, Reinaldo B. & Ferreira, Clécio S. & Genton, Marc G., 2018. "Scale and shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 98-110.
    6. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Abbas Mahdavi & Narayanaswamy Balakrishnan & Ahad Jamalizadeh, 2024. "Robust Classification via Finite Mixtures of Matrix Variate Skew- t Distributions," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    2. Naderi, Mehrdad & Tamandi, Mostafa & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2024. "Three-way data clustering based on the mean-mixture of matrix-variate normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).

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