IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v179y2020ics0047259x2030230x.html
   My bibliography  Save this article

Scale and shape mixtures of matrix variate extended skew normal distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2030230X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2020.104649?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    2. Sriya Anbil & Mark A. Carlson & Christopher Hanes & David C. Wheelock, 2020. "A New Daily Federal Funds Rate Series and History of the Federal Funds Market, 1928-1954," Finance and Economics Discussion Series 2020-059, Board of Governors of the Federal Reserve System (U.S.).
    3. Escobari, Diego & Garcia, Sergio & Mellado, Cristhian, 2017. "Identifying bubbles in Latin American equity markets: Phillips-Perron-based tests and linkages," Emerging Markets Review, Elsevier, vol. 33(C), pages 90-101.
    4. Xiong, Qian & Peng, Zuoxiang, 2020. "Asymptotic expansions of powered skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 158(C).
    5. D.A. Turkington, 1997. "Some results in matrix calculus and an example of their application to econometrics," Economics Discussion / Working Papers 97-07, The University of Western Australia, Department of Economics.
    6. Eugene N. White, 2004. "Bubbles and Busts: The 1990s in the Mirror of the 1920s," FRU Working Papers 2004/09, University of Copenhagen. Department of Economics. Finance Research Unit.
    7. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    8. Alina Sorescu & Sorin M. Sorescu & Will J. Armstrong & Bart Devoldere, 2018. "Two Centuries of Innovations and Stock Market Bubbles," Marketing Science, INFORMS, vol. 37(4), pages 507-529, August.
    9. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2019. "How Sensitive Are VAR Forecasts to Prior Hyperparameters? An Automated Sensitivity Analysis," Advances in Econometrics, in: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A, volume 40, pages 229-248, Emerald Group Publishing Limited.
    10. Lachos, Victor H. & Prates, Marcos O. & Dey, Dipak K., 2021. "Heckman selection-t model: Parameter estimation via the EM-algorithm," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    11. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    12. Hong Lan & Alexander Meyer-Gohde, 2013. "Pruning in Perturbation DSGE Models - Guidance from Nonlinear Moving Average Approximations," SFB 649 Discussion Papers SFB649DP2013-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    14. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    15. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
    16. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    17. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
    18. Sungduk Kim & Zhen Chen & Neil J. Perkins & Enrique F. Schisterman & Germaine M. Buck Louis, 2019. "A Model-Based Approach to Detection Limits in Studying Environmental Exposures and Human Fecundity," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 524-547, December.
    19. Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.
    20. Nicholas Crafts & Peter Fearon, 2010. "Lessons from the 1930s Great Depression," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 26(3), pages 285-317, Autumn.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x2030230x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.