IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i3p597-617.html
   My bibliography  Save this article

Two-sample tests based on empirical Hankel transforms

Author

Listed:
  • L. Baringhaus
  • D. Kolbe

Abstract

We study a new Cramér-von Mises type test for the general nonparametric two-sample problem on the nonnegative half-line. The test statistic is based on the empirical Hankel transforms of the sample variables, critical values are obtained by bootstrapping. The test is shown to be consistent against each fixed alternative. A scale invariant version of the test is also considered. A power comparison with the classical Cramér-von Mises test and another new Cramér-von Mises type test is done by simulation. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:597-617
    DOI: 10.1007/s00362-014-0599-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-014-0599-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-014-0599-1?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. Patrick Marsh, 2010. "A two-sample nonparametric likelihood ratio test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1053-1065.
    2. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    3. Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
    4. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.
    5. Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    6. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    7. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    8. Simos Meintanis, 2009. "A unified approach of testing for discrete and continuous Pareto laws," Statistical Papers, Springer, vol. 50(3), pages 569-580, June.
    9. Schmid, Friedrich & Trede, Mark, 1995. "A distribution free test for the two sample problem for general alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 409-419, October.
    10. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    11. M. V. Alba & D. Barrera & M. D. Jiménez, 2001. "A homogeneity test based on empirical characteristic functions," Computational Statistics, Springer, vol. 16(2), pages 255-270, July.
    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. Baringhaus, Ludwig & Gaigall, Daniel, 2023. "A goodness-of-fit test for the compound Poisson exponential model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    2. Judith H. Parkinson-Schwarz & Arne C. Bathke, 2022. "Testing for equality of distributions using the concept of (niche) overlap," Statistical Papers, Springer, vol. 63(1), pages 225-242, February.
    3. Li Cai & Suojin Wang, 2021. "Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing," Statistical Papers, Springer, vol. 62(6), pages 2573-2602, December.
    4. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    5. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.

    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. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    2. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    3. M. D. Jiménez-Gamero & J. L. Moreno-Rebollo & J. A. Mayor-Gallego, 2018. "On the estimation of the characteristic function in finite populations with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 95-121, March.
    4. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    5. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2015. "An approximation to the null distribution of a class of Cramér–von Mises statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 258-272.
    6. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    7. Baringhaus, Ludwig & Gaigall, Daniel, 2023. "A goodness-of-fit test for the compound Poisson exponential model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    8. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    9. Delgado, Miguel A. & Song, Xiaojun, 2018. "Nonparametric tests for conditional symmetry," Journal of Econometrics, Elsevier, vol. 206(2), pages 447-471.
    10. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    11. Norbert Henze & María Dolores Jiménez‐Gamero, 2021. "A test for Gaussianity in Hilbert spaces via the empirical characteristic functional," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 406-428, June.
    12. V. Alba Fernández & D. Barrera Rosillo & M. Ibáñez Pérez & M. Jiménez Gamero, 2009. "A homogeneity test for bivariate random variables," Computational Statistics, Springer, vol. 24(3), pages 513-531, August.
    13. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    14. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    15. Ansgar Steland, 2016. "Asymptotics for random functions moderated by dependent noise," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 363-387, October.
    16. Alba Fernández, M.V. & Jiménez Gamero, M.D. & Castillo Gutiérrez, S., 2014. "Approximating a class of goodness-of-fit test statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 24-38.
    17. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    18. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    19. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    20. Norbert Henze & Pierre Lafaye De Micheaux & Simos G. Meintanis, 2022. "Tests for circular symmetry of complex-valued random vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 488-518, June.

    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:stpapr:v:56:y:2015:i:3:p:597-617. 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.