IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v128y2014icp19-32.html
   My bibliography  Save this article

A test for multivariate skew-normality based on its canonical form

Author

Listed:
  • Balakrishnan, N.
  • Capitanio, A.
  • Scarpa, B.

Abstract

A test to assess if a sample comes from a multivariate skew-normal distribution is proposed. The test statistic is obtained from the canonical form of the multivariate skew-normal distribution and its null distribution is derived. The power of the proposed test is evaluated through Monte Carlo simulations for different conveniently chosen alternatives. Finally, three numerical examples are presented for the purpose of illustration.

Suggested Citation

  • Balakrishnan, N. & Capitanio, A. & Scarpa, B., 2014. "A test for multivariate skew-normality based on its canonical form," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 19-32.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:19-32
    DOI: 10.1016/j.jmva.2014.02.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000451
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.02.015?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. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    3. Simos G. Meintanis & Zdeněk Hlávka, 2010. "Goodness‐of‐Fit Tests for Bivariate and Multivariate Skew‐Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 701-714, December.
    4. Balakrishnan, N. & Scarpa, Bruno, 2012. "Multivariate measures of skewness for the skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 73-87, February.
    5. Adelchi Azzalini & Marc G. Genton & Bruno Scarpa, 2010. "Invariance-based estimating equations for skew-symmetric distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 275-298.
    6. Olvi L. Mangasarian & W. Nick Street & William H. Wolberg, 1995. "Breast Cancer Diagnosis and Prognosis Via Linear Programming," Operations Research, INFORMS, vol. 43(4), pages 570-577, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jorge M. Arevalillo & Hilario Navarro, 2019. "A stochastic ordering based on the canonical transformation of skew-normal vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 475-498, June.
    2. Abdi, Me’raj & Madadi, Mohsen & Balakrishnan, Narayanaswamy & Jamalizadeh, Ahad, 2021. "Family of mean-mixtures of multivariate normal distributions: Properties, inference and assessment of multivariate skewness," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    3. Baishuai Zuo & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions," Papers 2311.18176, arXiv.org.
    4. Jorge M. Arevalillo & Hilario Navarro, 2021. "Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    5. Elizabeth González-Estrada & José A. Villaseñor & Rocío Acosta-Pech, 2022. "Shapiro-Wilk test for multivariate skew-normality," Computational Statistics, Springer, vol. 37(4), pages 1985-2001, September.
    6. Jorge M. Arevalillo & Hilario Navarro, 2020. "Data projections by skewness maximization under scale mixtures of skew-normal vectors," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 435-461, June.
    7. Hashemi, Farzane & Naderi, Mehrdad & Jamalizadeh, Ahad & Bekker, Andriette, 2021. "A flexible factor analysis based on the class of mean-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

    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. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    2. Jorge M. Arevalillo & Hilario Navarro, 2019. "A stochastic ordering based on the canonical transformation of skew-normal vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 475-498, June.
    3. Jorge M. Arevalillo & Hilario Navarro, 2021. "Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    4. Mehdi Amiri & Ahad Jamalizadeh & Mina Towhidi, 2015. "Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution," Statistical Papers, Springer, vol. 56(4), pages 1071-1098, November.
    5. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    6. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Jorge M. Arevalillo & Hilario Navarro, 2020. "Data projections by skewness maximization under scale mixtures of skew-normal vectors," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 435-461, June.
    8. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    9. Mitchell, James & Weale, Martin, 2019. "Forecasting with Unknown Unknowns: Censoring and Fat Tails on the Bank of England's Monetary Policy Committee," EMF Research Papers 27, Economic Modelling and Forecasting Group.
    10. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    11. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    12. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    13. Douadia Bougherara & Laurent Piet, 2018. "On the role of probability weighting on WTP for crop insurance with and without yield skewness," Working Papers hal-02790605, HAL.
    14. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    15. Shushi, Tomer, 2018. "A proof for the existence of multivariate singular generalized skew-elliptical density functions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 50-55.
    16. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    17. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    18. Maximiano Pinheiro & Paulo Esteves, 2012. "On the uncertainty and risks of macroeconomic forecasts: combining judgements with sample and model information," Empirical Economics, Springer, vol. 42(3), pages 639-665, June.
    19. C. J. Adcock, 2023. "The Linear Skew-t Distribution and Its Properties," Stats, MDPI, vol. 6(1), pages 1-30, February.
    20. Adelchi Azzalini, 2012. "Selection models under generalized symmetry settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 737-750, August.

    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:128:y:2014:i:c:p:19-32. 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.