IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v26y2017i1d10.1007_s11749-016-0504-4.html
   My bibliography  Save this article

Robust asymptotic tests for the equality of multivariate coefficients of variation

Author

Listed:
  • Stephanie Aerts

    (HEC-ULg, University of Liege (ULg, N1))

  • Gentiane Haesbroeck

    (University of Liege (ULg, Polytech 1))

Abstract

In order to easily compare several populations on the basis of more than one feature, multivariate coefficients of variation (MCV) may be used as they allow to summarize relative dispersion in a single index. However, up to date, no test of equality of one or more MCVs has been developed in the literature. In this paper, several classical and robust Wald-type tests are proposed and studied. The asymptotic distributions of the test statistics are derived under elliptical symmetry, and the asymptotic efficiency of the robust versions is compared to the classical tests. Robustness of the proposed procedures is examined through partial and joint influence functions of the test statistic, as well as by means of power and level influence functions. A simulation study compares the performance of the classical and robust tests under uncontaminated and contaminated schemes, and the difference with the usual covariance homogeneity test is highlighted. As a by-product, these tests may also be considered in the univariate context where they yield procedures that are both robust and easy-to-use. They provide an interesting alternative to the numerous parametric tests existing in the literature, which are, in most cases, unreliable in presence of outliers. The methods are illustrated on a real data set.

Suggested Citation

  • Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0504-4
    DOI: 10.1007/s11749-016-0504-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-016-0504-4
    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/s11749-016-0504-4?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. Ghosh, Abhik & Mandal, Abhijit & Martín, Nirian & Pardo, Leandro, 2016. "Influence analysis of robust Wald-type tests," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 102-126.
    2. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    3. A. García-Pérez, 2012. "A linear approximation to the power function of a test," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 855-875, October.
    4. K. Krishnamoorthy & Meesook Lee, 2014. "Improved tests for the equality of normal coefficients of variation," Computational Statistics, Springer, vol. 29(1), pages 215-232, February.
    5. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    6. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    7. Hallin, Marc & Paindaveine, Davy, 2009. "Optimal tests for homogeneity of covariance, scale, and shape," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 422-444, March.
    8. Cator, Eric A. & Lopuhaä, Hendrik P., 2010. "Asymptotic expansion of the minimum covariance determinant estimators," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2372-2388, November.
    9. Krishnamoorthy, K. & Yu, Jianqi, 2004. "Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 161-169, January.
    10. Aerts, S. & Haesbroeck, G. & Ruwet, C., 2015. "Multivariate coefficients of variation: Comparison and influence functions," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 183-198.
    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. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
    3. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    4. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.

    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. Ayanendranath Basu & Abhijit Mandal & Nirian Martín & Leandro Pardo, 2019. "A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 85-107, March.
    2. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    3. Yunlu Jiang & Canhong Wen & Xueqin Wang, 2018. "Adaptive Exponential Power Depth with Application to Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 466-480, October.
    4. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    5. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    6. Paindaveine, Davy & Van Bever, Germain, 2014. "Inference on the shape of elliptical distributions based on the MCD," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 125-144.
    7. Frahm, Gabriel, 2009. "Asymptotic distributions of robust shape matrices and scales," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1329-1337, August.
    8. Davy Paindaveine & Germain Van Bever, 2013. "Inference on the Shape of Elliptical Distribution Based on the MCD," Working Papers ECARES ECARES 2013-27, ULB -- Universite Libre de Bruxelles.
    9. Pere, Jaakko & Ilmonen, Pauliina & Viitasaari, Lauri, 2024. "On extreme quantile region estimation under heavy-tailed elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    10. Laniado Rodas, Henry, 2017. "Multivariate outlier detection based on a robust Mahalanobis distance with shrinkage estimators," DES - Working Papers. Statistics and Econometrics. WS 24613, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    12. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    13. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    14. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    15. Nathan Lassance & Victor DeMiguel & Frédéric Vrins, 2022. "Optimal Portfolio Diversification via Independent Component Analysis," Operations Research, INFORMS, vol. 70(1), pages 55-72, January.
    16. Liusha Yang & Romain Couillet & Matthew R. McKay, 2015. "A Robust Statistics Approach to Minimum Variance Portfolio Optimization," Papers 1503.08013, arXiv.org.
    17. Sleire, Anders D. & Støve, Bård & Otneim, Håkon & Berentsen, Geir Drage & Tjøstheim, Dag & Haugen, Sverre Hauso, 2022. "Portfolio allocation under asymmetric dependence in asset returns using local Gaussian correlations," Finance Research Letters, Elsevier, vol. 46(PB).
    18. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2016. "Efficient skewness/semivariance portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 331-346, September.
    19. Seyoung Park & Eun Ryung Lee & Sungchul Lee & Geonwoo Kim, 2019. "Dantzig Type Optimization Method with Applications to Portfolio Selection," Sustainability, MDPI, vol. 11(11), pages 1-32, June.
    20. McDowell, Shaun, 2018. "An empirical evaluation of estimation error reduction strategies applied to international diversification," Journal of Multinational Financial Management, Elsevier, vol. 44(C), pages 1-13.

    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:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0504-4. 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.