IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v102y2015i2p479-485..html
   My bibliography  Save this article

Effective degrees of freedom: a flawed metaphor

Author

Listed:
  • Lucas Janson
  • William Fithian
  • Trevor J. Hastie

Abstract

To most applied statisticians, a fitting procedure’s degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, the degrees of freedom is often used to parameterize the bias-variance trade-off in model selection. We argue that, on the contrary, model complexity and degrees of freedom may correspond very poorly. We exhibit and theoretically explore various fitting procedures for which the degrees of freedom is not monotonic in the model complexity parameter and can exceed the total dimension of the ambient space even in very simple settings. We show that the degrees of freedom for any nonconvex projection method can be unbounded.

Suggested Citation

  • Lucas Janson & William Fithian & Trevor J. Hastie, 2015. "Effective degrees of freedom: a flawed metaphor," Biometrika, Biometrika Trust, vol. 102(2), pages 479-485.
  • Handle: RePEc:oup:biomet:v:102:y:2015:i:2:p:479-485.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asv019
    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. Andrew L. Hicks & Mark S. Handcock & Narayan Sastry & Anne R. Pebley, 2018. "Sequential Neighborhood Effects: The Effect of Long-Term Exposure to Concentrated Disadvantage on Children’s Reading and Math Test Scores," Demography, Springer;Population Association of America (PAA), vol. 55(1), pages 1-31, February.
    2. Lasanthi C. R. Pelawa Watagoda & David J. Olive, 2021. "Comparing six shrinkage estimators with large sample theory and asymptotically optimal prediction intervals," Statistical Papers, Springer, vol. 62(5), pages 2407-2431, October.
    3. Iacopo Bernetti & Veronica Alampi Sottini & Lorenzo Bambi & Elena Barbierato & Tommaso Borghini & Irene Capecchi & Claudio Saragosa, 2020. "Urban Niche Assessment: An Approach Integrating Social Media Analysis, Spatial Urban Indicators and Geo-Statistical Techniques," Sustainability, MDPI, vol. 12(10), pages 1-26, May.
    4. Daniel A. Griffith & Yongwan Chun, 2016. "Evaluating Eigenvector Spatial Filter Corrections for Omitted Georeferenced Variables," Econometrics, MDPI, vol. 4(2), pages 1-12, June.
    5. Daniel Durstewitz, 2017. "A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-33, June.
    6. Philip T. Reiss & Lei Huang & Pei‐Shien Wu & Huaihou Chen & Stan Colcombe, 2017. "Pointwise influence matrices for functional‐response regression," Biometrics, The International Biometric Society, vol. 73(4), pages 1092-1101, December.

    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:102:y:2015:i:2:p:479-485.. 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.