IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v96y2009i1p133-148.html
   My bibliography  Save this article

Model checking in regression via dimension reduction

Author

Listed:
  • Yingcun Xia

Abstract

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern. Consistency of the method is proved for parametric and semiparametric regression models. A bootstrap implementation is also discussed. Simulation comparisons with several existing methods are made, suggesting that the proposed methods are more efficient than the existing methods when the dimension increases. Air pollution data from Chicago are used to illustrate the procedure. Copyright 2009, Oxford University Press.

Suggested Citation

  • Yingcun Xia, 2009. "Model checking in regression via dimension reduction," Biometrika, Biometrika Trust, vol. 96(1), pages 133-148.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:133-148
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asn074
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chiang, Chin-Tsang & Chiu, Chih-Heng, 2012. "Nonparametric and semiparametric optimal transformations of markers," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 124-141, January.
    2. Chiang, Chin-Tsang & Huang, Ming-Yueh & Bai, Ren-Hong, 2013. "Binary response models with M-phase case-control data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 332-348.
    3. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    4. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    5. Chen, Feifei & Jiang, Qing & Feng, Zhenghui & Zhu, Lixing, 2020. "Model checks for functional linear regression models based on projected empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Chin-Shang Li & Minggen Lu, 2018. "A lack-of-fit test for generalized linear models via single-index techniques," Computational Statistics, Springer, vol. 33(2), pages 731-756, June.
    7. Zhang, Yaowu & Zhou, Yeqing & Zhu, Liping, 2024. "A post-screening diagnostic study for ultrahigh dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).

    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:oup:biomet:v:96:y:2009:i:1:p:133-148. 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.

    We have no bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.