IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp193-208.html
   My bibliography  Save this article

On an independence test approach to the goodness-of-fit problem

Author

Listed:
  • Baringhaus, Ludwig
  • Gaigall, Daniel

Abstract

Let X1,…,Xn be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R2→R and g:R2→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X1,X2),g(X1,X2) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xi,Xj),g(Xi,Xj)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.

Suggested Citation

  • Baringhaus, Ludwig & Gaigall, Daniel, 2015. "On an independence test approach to the goodness-of-fit problem," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 193-208.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:193-208
    DOI: 10.1016/j.jmva.2015.05.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001402
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.05.013?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. Schneemeier, Wilhelm, 1989. "Weak convergence and Glivenko-Cantelli results for empirical processes of u-statistic structure," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 325-334, December.
    3. Helena Jansen Van Rensburg & Jan Swanepoel, 2008. "A class of goodness-of-fit tests based on a new characterization of the exponential distribution," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 539-551.
    4. Norbert Henze & Bernhard Klar, 2002. "Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 425-444, June.
    5. Baringhaus, L. & Henze, N., 2008. "A new weighted integral goodness-of-fit statistic for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1006-1016, June.
    6. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    7. Truc Nguyen & Khoan Dinh, 2003. "Characterizations of normal distributions and EDF goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 149-157, September.
    8. Tea-Yuan Hwang & Chin-Yuan Hu, 1999. "On a Characterization of the Gamma Distribution: The Independence of the Sample Mean and the Sample Coefficient of Variation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 749-753, December.
    9. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
    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. Steffen Betsch & Bruno Ebner, 2019. "A new characterization of the Gamma distribution and associated goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 779-806, October.
    2. James S. Allison & Steffen Betsch & Bruno Ebner & Jaco Visagie, 2022. "On Testing the Adequacy of the Inverse Gaussian Distribution," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    3. Bojana Milošević & Marko Obradović, 2016. "Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 413-427, 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. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    2. Meintanis, Simos G., 2008. "A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2496-2503, January.
    3. Arcones, Miguel A. & Wang, Yishi, 2006. "Some new tests for normality based on U-processes," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 69-82, January.
    4. 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.
    5. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    6. 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.
    7. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.
    8. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    9. José A. Villaseñor & Elizabeth González-Estrada & Adrián Ochoa, 2019. "On Testing the Inverse Gaussian Distribution Hypothesis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 60-74, June.
    10. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    11. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    12. Lee, Sangyeol & Oh, Haejune, 2015. "Entropy test and residual empirical process for autoregressive conditional duration models," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 1-12.
    13. Zacharias Psaradakis & Marián Vávra, 2017. "Normality Tests for Dependent Data: Large-Sample and Bootstrap Approaches," Birkbeck Working Papers in Economics and Finance 1706, Birkbeck, Department of Economics, Mathematics & Statistics.
    14. Kley, Oliver & Klüppelberg, Claudia & Paterlini, Sandra, 2020. "Modelling extremal dependence for operational risk by a bipartite graph," Journal of Banking & Finance, Elsevier, vol. 117(C).
    15. 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.
    16. 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.
    17. Székely, Gábor J. & Rizzo, Maria L., 2004. "Mean distance test of Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 241-247, April.
    18. Graciela Boente & Daniela Rodriguez & Wenceslao González Manteiga, 2014. "Goodness-of-fit Test for Directional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 259-275, March.
    19. 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.
    20. 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).
    21. Kheifets, Igor & Velasco, Carlos, 2017. "New goodness-of-fit diagnostics for conditional discrete response models," Journal of Econometrics, Elsevier, vol. 200(1), pages 135-149.

    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:140:y:2015:i:c:p:193-208. 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.