IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v10y1994i02p316-356_00.html
   My bibliography  Save this article

Testing the Goodness of Fit of a Parametric Density Function by Kernel Method

Author

Listed:
  • Fan, Yanqin

Abstract

Let F denote a distribution function defined on the probability space (Ω,null, P ), which is absolutely continuous with respect to the Lebesgue measure in R with probability density function f . Let f 0 (·,β) be a parametric density function that depends on an unknown p × 1 vector β. In this paper, we consider tests of the goodness-of-fit of f 0 (·,β) for f (·) for some β based on (i) the integrated squared difference between a kernel estimate of f (·) and the quasimaximum likelihood estimate of f 0 (·,β) denoted by I and (ii) the integrated squared difference between a kernel estimate of f (·) and the corresponding kernel smoothed estimate of f 0 (·, β) denoted by J . It is shown in this paper that the amount of smoothing applied to the data in constructing the kernel estimate of f (·) determines the form of the test statistic based on I . For each test developed, we also examine its asymptotic properties including consistency and the local power property. In particular, we show that tests developed in this paper, except the first one, are more powerful than the Kolmogorov-Smirnov test under the sequence of local alternatives introduced in Rosenblatt [12], although they are less powerful than the Kolmogorov-Smirnov test under the sequence of Pitman alternatives. A small simulation study is carried out to examine the finite sample performance of one of these tests.

Suggested Citation

  • Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  • Handle: RePEc:cup:etheor:v:10:y:1994:i:02:p:316-356_00
    as

    Download full text from publisher

    File URL: http://journals.cambridge.org/abstract_S0266466600008434
    File Function: link to article abstract page
    Download Restriction: no

    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:cup:etheor:v:10:y:1994:i:02:p:316-356_00. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: http://journals.cambridge.org/jid_ECT .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.