IDEAS home Printed from
   My bibliography  Save this article

A Theorem on Uniform Convergence of Stochastic Functions with Applications


  • Yuan, Ke-Hai


In a variety of statistical problems one needs to manipulate a sequence of stochastic functions involving some unknown parameters. The asymptotic behavior of the estimated parameters often depends on the asymptotic properties of such functions. Especially, the consistency of the estimated parameters follows from the uniform convergence of the sequence of stochastic functions. A theorem on uniform convergence of a sequence of vector valued random functions is presented. The forms of these functions are very general and the assumptions are rather natural. If the sequence of random functions is generated by a sequence of random vectors, these random vectors are only required to be independently distributed and can be of different dimensions. As applications, we consider the consistency of the estimated regression parameters in logistic regression and in M-estimation in a linear model.

Suggested Citation

  • Yuan, Ke-Hai, 1997. "A Theorem on Uniform Convergence of Stochastic Functions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 100-109, July.
  • Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:100-109

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Cheng, Ching-Shui & Li, Ker-Chau, 1984. "The strong consistency of M-estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 91-98, August.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Bai, Yang & Fung, Wing K. & Zhu, Zhong Yi, 2009. "Penalized quadratic inference functions for single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 152-161, January.
    2. Ke-Hai Yuan & Robert Jennrich, 2000. "Estimating Equations with Nuisance Parameters: Theory and Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 343-350, June.


    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:eee:jmvana:v:62:y:1997:i:1:p:100-109. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.