IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2003cf226.html
   My bibliography  Save this paper

Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE

Author

Listed:
  • Muneya Matsui

    (Graduate School of Economics, The University of Tokyo)

  • Akimichi Takemura

    (Department of Mathematical Informatics, University of Tokyo)

Abstract

We consider goodness-of-fit tests of Cauchy distribution based on weighted integrals of the squared distance of the difference between the empirical characteristic function of the standardized data and the characteristic function of the standard Cauchy distribution. For standardization of data Gurtler and Henze (2000) used the median and the interquartile range. In this paper we use maximum likelihood estimator (MLE)and an equivariant integrated squared error estimator (EISE), which minimizes the weighted integral. We derive an explicit form of the asymptotic covariance function of the characteristic function process with parameters estimated by MLE or EISE. The eigenvalues of the covariance function are numerically evaluated and the asymptotic distribution of the test statistics are obtained by the residue theorem. Simulation study shows that the proposed tests compare well to tests proposed by Gurtler and Henze (2000) and more traditional tests based on the empirical distribution function.

Suggested Citation

  • Muneya Matsui & Akimichi Takemura, 2003. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," CIRJE F-Series CIRJE-F-226, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2003cf226
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2003/2003cf226.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Besbeas, Panagiotis & Morgan, Byron J. T., 2001. "Integrated squared error estimation of Cauchy parameters," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 397-401, December.
    2. Nora Gürtler & Norbert Henze, 2000. "Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 267-286, June.
    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. Yuichi Akaoka & Kazuki Okamura & Yoshiki Otobe, 2022. "Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 895-923, October.
    2. Muneya Matsui & Akimichi Takemura, 2005. "Goodness-of-Fit Tests for Symmetric Stable Distributions - Empirical Characteristic Function Approach," CIRJE F-Series CIRJE-F-384, CIRJE, Faculty of Economics, University of Tokyo.
    3. 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.
    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. Meintanis, S. & Ushakov, N. G., 2004. "Binned goodness-of-fit tests based on the empirical characteristic function," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 305-314, September.
    6. 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.
    7. 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.
    8. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    9. 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.
    10. Henze, N. & Klar, B. & Zhu, L. X., 2005. "Checking the adequacy of the multivariate semiparametric location shift model," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 238-256, April.
    11. 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.
    12. 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.
    13. Klar, Bernhard & Meintanis, Simos G., 2005. "Tests for normal mixtures based on the empirical characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 227-242, April.
    14. Besbeas, Panagiotis & Morgan, Byron J. T., 2004. "Integrated squared error estimation of normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 517-526, January.
    15. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    16. Besbeas, Panagiotis & J.T. Morgan, Byron, 2004. "Efficient and robust estimation for the one-sided stable distribution of index," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 251-257, February.
    17. Muneya Matsui & Akimichi Takemura, 2005. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 183-199, March.
    18. Simos Meintanis & Bojana Milošević & Marko Obradović, 2023. "Bahadur efficiency for certain goodness-of-fit tests based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 723-751, October.
    19. Michael Rockinger & Maria Semenova, 2005. "Estimation of Jump-Diffusion Process vis Empirical Characteristic Function," FAME Research Paper Series rp150, International Center for Financial Asset Management and Engineering.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tky:fseres:2003cf226. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    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.