IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v82y2019i5d10.1007_s00184-018-0682-z.html
   My bibliography  Save this article

Box–Cox elliptical distributions with application

Author

Listed:
  • Raúl Alejandro Morán-Vásquez

    (University of Antioquia)

  • Silvia L. P. Ferrari

    (University of São Paulo)

Abstract

We propose and study the class of Box–Cox elliptical distributions. It provides alternative distributions for modeling multivariate positive, marginally skewed and possibly heavy-tailed data. This new class of distributions has as a special case the class of log-elliptical distributions, and reduces to the Box–Cox symmetric class of distributions in the univariate setting. The parameters are interpretable in terms of quantiles and relative dispersions of the marginal distributions and of associations between pairs of variables. The relation between the scale parameters and quantiles makes the Box–Cox elliptical distributions attractive for regression modeling purposes. Applications to data on vitamin intake are presented and discussed.

Suggested Citation

  • Raúl Alejandro Morán-Vásquez & Silvia L. P. Ferrari, 2019. "Box–Cox elliptical distributions with application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 547-571, July.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0682-z
    DOI: 10.1007/s00184-018-0682-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-018-0682-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-018-0682-z?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. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    2. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    3. Vlasios Voudouris & Robert Gilchrist & Robert Rigby & John Sedgwick & Dimitrios Stasinopoulos, 2012. "Modelling skewness and kurtosis with the BCPE density in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1279-1293, November.
    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. Yue, Chen & Chen, Shaojie & Sair, Haris I. & Airan, Raag & Caffo, Brian S., 2015. "Estimating a graphical intra-class correlation coefficient (GICC) using multivariate probit-linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 126-133.
    2. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    3. Klaus Müller & Wolf-Dieter Richter, 2019. "On p-generalized elliptical random processes," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-37, December.
    4. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.
    5. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    6. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2022. "Some properties of the unified skew-normal distribution," Statistical Papers, Springer, vol. 63(2), pages 461-487, April.
    7. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 15/13, Institute for Fiscal Studies.
    8. Cruz Lopez, Jorge A. & Harris, Jeffrey H. & Hurlin, Christophe & Pérignon, Christophe, 2017. "CoMargin," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(5), pages 2183-2215, October.
      • Jorge A. Cruz Lopez & Jeffrey H. Harris & Christophe Hurlin & Christophe Pérignon, 2015. "CoMargin," Working Papers halshs-00979440, HAL.
      • Jorge Cruz Lopez & Jeffrey Harris & Christophe Hurlin & Christophe Pérignon, 2017. "CoMargin," Post-Print hal-03579309, HAL.
    9. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    10. Fernanda De Bastiani & Robert A. Rigby & Dimitrios M. Stasinopoulous & Audrey H.M.A. Cysneiros & Miguel A. Uribe-Opazo, 2018. "Gaussian Markov random field spatial models in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 168-186, January.
    11. Kashyap, Ravi, 2019. "The perfect marriage and much more: Combining dimension reduction, distance measures and covariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2021. "A formulation for continuous mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    13. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.
    14. Camba-Méndez, Gonzalo & Rodriguez-Palenzuela, Diego & Carbó-Valverde, Santiago, 2014. "Financial reputation, market interventions and debt issuance by banks: a truncated two-part model approach," Working Paper Series 1741, European Central Bank.
    15. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2021. "Forecasting with Shadow-Rate VARs," Working Papers 21-09, Federal Reserve Bank of Cleveland.
    16. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    17. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.
    18. C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.
    19. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 41/13, Institute for Fiscal Studies.
    20. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.

    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:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0682-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.