IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-99-0803-5_11.html
   My bibliography  Save this book chapter

An Analog of the Bickel–Rosenblatt Test for Error Density in the Linear Regression Model

In: Research Papers in Statistical Inference for Time Series and Related Models

Author

Listed:
  • Fuxia Cheng

    (Illinois State University)

  • Hira L. Koul

    (Michigan State University)

  • Nao Mimoto

    (The University of Akron)

  • Narayana Balakrishna

    (Cochin University of Science and Technology)

Abstract

This paper addresses the problem of testing the goodness-of-fit hypothesis pertaining to error density in multiple linear regression models with non-random and random predictors. The proposed tests are based on the integrated square difference between a nonparametric density estimator based on the residuals and its expected value under the null hypothesis when all regression parameters are known. We derive the asymptotic distributions of this sequence of test statistics under the null hypothesis and under certain global alternatives. The asymptotic null distribution of a suitably standardized test statistic based on the residuals is the same as in the case of known underlying regression parameters. Under the global $$L_2$$ L 2 alternatives of [2], the asymptotic distribution of this sequence of statistics is affected by not knowing the parameters and, in general, is different from the one obtained in [2] for the zero intercept linear autoregressive time series context.

Suggested Citation

  • Fuxia Cheng & Hira L. Koul & Nao Mimoto & Narayana Balakrishna, 2023. "An Analog of the Bickel–Rosenblatt Test for Error Density in the Linear Regression Model," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 291-323, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_11
    DOI: 10.1007/978-981-99-0803-5_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-981-99-0803-5_11. 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: 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.