IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v106y2019i2p385-400..html
   My bibliography  Save this article

Bootstrap of residual processes in regression: to smooth or not to smooth?

Author

Listed:
  • N Neumeyer
  • I Van Keilegom

Abstract

SummaryIn this paper we consider regression models with centred errors, independent of the covariates. Given independent and identically distributed data and given an estimator of the regression function, which can be parametric or nonparametric in nature, we estimate the distribution of the error term by the empirical distribution of estimated residuals. To approximate the distribution of this estimator, Koul & Lahiri (1994) and Neumeyer (2009) proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples. So far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context. Here we solve this open problem and show that the nonsmooth residual bootstrap is consistent. We illustrate the theoretical result by means of simulations, which demonstrate the accuracy of this bootstrap procedure for various models, testing procedures and sample sizes.

Suggested Citation

  • N Neumeyer & I Van Keilegom, 2019. "Bootstrap of residual processes in regression: to smooth or not to smooth?," Biometrika, Biometrika Trust, vol. 106(2), pages 385-400.
    • Handle: RePEc:oup:biomet:v:106:y:2019:i:2:p:385-400.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asz009
    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. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).

    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:106:y:2019:i:2:p:385-400.. 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.