IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v78y2016i2d10.1007_s13171-016-0085-z.html
   My bibliography  Save this article

Asymptotics for Regression Models Under Loss of Identifiability

Author

Listed:
  • Joseph Rynkiewicz

    (Université de Paris 1)

Abstract

This paper discusses the asymptotic behavior of regression models under general conditions, especially if the dimensionality of the set of true parameters is larger than zero and the true model is not identifiable. Firstly, we give a general inequality for the difference of the sum of square errors (SSE) of the estimated regression model and the SSE of the theoretical true regression function in our model. A set of generalized derivative functions is a key tool in deriving such inequality. Under suitable Donsker condition for this set, we provide the asymptotic distribution for the difference of SSE. We show how to get this Donsker property for parametric models even though the parameters characterizing the best regression function are not unique. This result is applied to neural networks regression models with redundant hidden units when loss of identifiability occurs and gives some hints on how penalizing such models to avoid over-fitting.

Suggested Citation

  • Joseph Rynkiewicz, 2016. "Asymptotics for Regression Models Under Loss of Identifiability," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 155-179, August.
    • Handle: RePEc:spr:sankha:v:78:y:2016:i:2:d:10.1007_s13171-016-0085-z
    DOI: 10.1007/s13171-016-0085-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-016-0085-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-016-0085-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Jian-Feng Yao, 2000. "On Least Squares Estimation for Stable Nonlinear AR Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 316-331, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Zhibiao, 2010. "Density estimation for nonlinear parametric models with conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 155(1), pages 71-82, March.

    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:sankha:v:78:y:2016:i:2:d:10.1007_s13171-016-0085-z. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.