IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/06-20.html
   My bibliography  Save this paper

Data Driven Likelihood Ratio Tests for Goodness-of-Fit with Estimated Parameters

Author

Listed:
  • Patrick Marsh

Abstract

This paper generalizes the goodness of fit tests of Claeskens and Hjort (2004) and Marsh (2006) to the case where the hypothesis specifies only family of distributions. Data driven versions of these tests are based upon the Akaike and Bayesian selection criteria. The asymptotic distributions of these tests are shown to be standard, unlike those based upon the empirical distribution function. Moreover, numerical evidence suggests that under the null hypothesis performance is very similar to tests such as the Kolmogorov-Smirnov or Anderson-Darling. However, in terms of power under the alternative, the proposed tests seem to have a consistent and significant advantage.

Suggested Citation

  • Patrick Marsh, 2006. "Data Driven Likelihood Ratio Tests for Goodness-of-Fit with Estimated Parameters," Discussion Papers 06/20, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:06/20
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2006/0620.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gerda Claeskens & Nils Lid Hjort, 2004. "Goodness of Fit via Non‐parametric Likelihood Ratios," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 487-513, December.
    2. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2005. "Bootstrapping modified goodness-of-fit statistics with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 111-121, February.
    3. Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
    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. Patrick Marsh, 2019. "Nonparametric conditional density specification testing and quantile estimation; with application to S&P500 returns," Discussion Papers 19/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    2. Patrick Marsh, 2010. "A two-sample nonparametric likelihood ratio test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1053-1065.
    3. Patrick Marsh, 2019. "Nonparametric series density estimation and testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 77-99, March.
    4. Olivier Thas, 2009. "Comments on: Goodness-of-fit tests in mixed modes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 260-264, August.
    5. Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    6. Best, D.J. & Rayner, J.C.W. & Thas, O., 2008. "Comparison of some tests of fit for the Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5338-5343, August.
    7. Perera, Indeewara & Silvapulle, Mervyn J., 2021. "Bootstrap based probability forecasting in multiplicative error models," Journal of Econometrics, Elsevier, vol. 221(1), pages 1-24.
    8. Gerda Claeskens & Jeffrey Hart, 2009. "Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 213-239, August.
    9. Consentino, Fabrizio & Claeskens, Gerda, 2010. "Order selection tests with multiply imputed data," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2284-2295, October.
    10. Fang, Ying & Li, Qi & Wu, Ximing & Zhang, Daiqiang, 2015. "A data-driven smooth test of symmetry," Journal of Econometrics, Elsevier, vol. 188(2), pages 490-501.
    11. Emiliano, Paulo C. & Vivanco, Mário J.F. & de Menezes, Fortunato S., 2014. "Information criteria: How do they behave in different models?," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 141-153.
    12. J. Beirlant & G. Claeskens & C. Croux & H. Degryse & H. Dewachter & G. Dhaene & J. Dhaene & I. Gijbels & M. Goovaerts & M. Hubert & F. Roodhooft & W. Schouten & M. Willekens, 2005. "Managing Uncertainty: Financial, Actuarial and Statistical Modeling," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(1), pages 23-48.
    13. Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
    14. Nicolai Bissantz & Gerda Claeskens & Hajo Holzmann & Axel Munk, 2009. "Testing for lack of fit in inverse regression—with applications to biophotonic imaging," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 25-48, January.
    15. 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.
    16. Ali Charkhi & Gerda Claeskens, 2018. "Asymptotic post-selection inference for the Akaike information criterion," Biometrika, Biometrika Trust, vol. 105(3), pages 645-664.
    17. Hart, Jeffrey D. & Choi, Taeryon & Yi, Seongbaek, 2016. "Frequentist nonparametric goodness-of-fit tests via marginal likelihood ratios," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 120-132.

    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:yor:yorken:06/20. 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: Paul Hodgson (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.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.