IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v90y2003i1p223-232.html
   My bibliography  Save this article

A test for linear versus convex regression function using shape-restricted regression

Author

Listed:
  • Mary C. Meyer

Abstract

An unbiased test for the appropriateness of the simple linear regression model is presented. The null hypothesis is that the underlying regression function is indeed a line, and the alternative is that it is convex. The exact distribution for a likelihood ratio test statistic is that of a mixture of beta random variables, with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction. Simulations show that the power of the test is favourable compared with the usual F-test against a quadratic model, for some nonquadratic choices of the underlying regression function. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Mary C. Meyer, 2003. "A test for linear versus convex regression function using shape-restricted regression," Biometrika, Biometrika Trust, vol. 90(1), pages 223-232, March.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:1:p:223-232
    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 search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Meyer, Mary C. & Wang, Jianqiang C., 2012. "Improved power of one-sided tests," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1619-1622.
    2. Quinn, Barry & Gallagher, Ronan & Kuosmanen, Timo, 2021. "Lurking in the Shadows: The Impact of Emissions Target Setting on Carbon Pricing and Environmental Efficiency," QBS Working Paper Series 2021/05, Queen's University Belfast, Queen's Business School.
    3. Liao, Xiyue & Meyer, Mary C., 2014. "coneproj: An R Package for the Primal or Dual Cone Projections with Routines for Constrained Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i12).
    4. Na Li & Xingzhong Xu & Pei Jin, 2011. "Testing the linearity in partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 99-114.
    5. Quinn, Barry & Gallagher, Ronan & Kuosmanen, Timo, 2023. "Lurking in the shadows: The impact of CO2 emissions target setting on carbon pricing in the Kyoto agreement period," Energy Economics, Elsevier, vol. 118(C).
    6. Keshvari, Abolfazl, 2017. "A penalized method for multivariate concave least squares with application to productivity analysis," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1016-1029.
    7. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, August.

    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:90:y:2003:i:1:p:223-232. 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.