IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v25y2013i2p487-498.html
   My bibliography  Save this article

Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks

Author

Listed:
  • Hammou El Barmi
  • Lahcen El Bermi

Abstract

A random variable X with cumulative distribution function F is said to have a symmetric distribution about θ if and only if X - θ and - X +θ are identically distributed. Different types of partial skewness and one-sided bias are obtained by looking at different types of orderings between the distributions of X - θ and - X +θ. For example, X , or equivalently F , is said to have type I bias about θ if X - θ is stochastically larger than - X +θ. In this paper, we assume that F is continuous, θ is known and develops an empirical likelihood ratio type test for testing for symmetry about θ against this type of alternative. This test is shown to be asymptotically distribution free and the results of a simulation study show that it outperforms in terms of power, a test developed for the same problem in Alfieri and El Barmi [(2005), 'Nonparametric Estimation of a Distribution Function with Type I Bias with Applications to Competing Risks', Journal of Nonparametric Statistics , 17, 319-333]. It turns out that the results developed here can be extended in a natural way to compare the sub-survival functions corresponding to two risks in a competing risks setting. We show how this can be done and illustrate our theoretical results with a real life example.

Suggested Citation

  • Hammou El Barmi & Lahcen El Bermi, 2013. "Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 487-498, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:487-498
    DOI: 10.1080/10485252.2013.772177
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2013.772177
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2013.772177?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. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    2. Richard Dykstra & Subhash Kochar & Tim Robertson, 1995. "Likelihood ratio tests for symmetry against one-sided alternatives," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 719-730, December.
    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. Narayanaswamy Balakrishnan & Laurent Bordes & Christian Paroissin & Jean-Christophe Turlot, 2016. "Single change-point detection methods for small lifetime samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 531-551, July.
    2. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    3. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    4. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    5. repec:jss:jstsof:28:i03 is not listed on IDEAS
    6. Zou, Changliang & Liu, Yukun & Qin, Peng & Wang, Zhaojun, 2007. "Empirical likelihood ratio test for the change-point problem," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 374-382, February.
    7. John Einmahl & Maria Gantner, 2012. "Testing for bivariate spherical symmetry," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 54-73, March.
    8. Michal Jakubczyk, 2016. "Choosing from multiple alternatives in cost-effectiveness analysis with fuzzy willingness-to-pay/accept and uncertainty," KAE Working Papers 2016-006, Warsaw School of Economics, Collegium of Economic Analysis.
    9. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    10. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    11. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics and Public Policy Working Papers 2010-28, University of Adelaide, School of Economics and Public Policy.
    12. Koning, A.J. & Peng, L., 2005. "Goodness-of-fit tests for a heavy tailed distribution," Econometric Institute Research Papers EI 2005-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Rodríguez-Martínez, C.M. & Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2021. "A multi-scale symmetry analysis of uninterrupted trends returns in daily financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    14. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Discussion Paper 2023-001, Tilburg University, Center for Economic Research.
    15. Fernández-Durán Juan José & Gregorio-Domínguez María Mercedes, 2023. "Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear data," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-17, January.
    16. Kiwitt, Sebastian & Nagel, Eva-Renate & Neumeyer, Natalie, 2005. "Empirical likelihood estimators for the error distribution in nonparametric regression models," Technical Reports 2005,45, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. Haywood, John & Khmaladze, Estate, 2008. "On distribution-free goodness-of-fit testing of exponentiality," Journal of Econometrics, Elsevier, vol. 143(1), pages 5-18, March.
    18. C. M. Rodr'iguez-Mart'inez & H. F. Coronel-Brizio & A. R. Hern'andez-Montoya, 2019. "A multi-scale symmetry analysis of uninterrupted trends returns of daily financial indices," Papers 1908.11204, arXiv.org.
    19. Bagkavos, D. & Patil, P.N., 2017. "A new test of independence for bivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 117-133.
    20. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Other publications TiSEM 261583f5-c571-48c6-8cea-9, Tilburg University, School of Economics and Management.
    21. Ping Ye & Bhaskar Bhattacharya, 2011. "Tests of symmetry with one-sided alternatives in three-way contingency tables," Statistical Papers, Springer, vol. 52(1), pages 33-51, February.
    22. Shen, Gang, 2013. "On empirical likelihood inference of a change-point," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1662-1668.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:25:y:2013:i:2:p:487-498. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.