IDEAS home Printed from
   My bibliography  Save this article

The Glivenko-Cantelli theorem based on data with randomly imputed missing values


  • Mojirsheibani, Majid


Glivenko-Cantelli-type results will be derived for the performance of the empirical distribution function under imputation of the missing data in the univariate case, when there are no auxiliary covariates. According to these results, both random imputation and the adjusted random imputation produce reliable estimates of the unknown distribution function. They are reliable in the sense that the corresponding empirical distribution functions stay (w.p.1) "close" to F(t), uniformly over t. At the same time, it is also shown that if r(n)[less-than-or-equals, slant]n is the number of nonmissing observations, then one cannot improve on the performance of the empirical distribution function Fr(n) by generating artificial data, in order to increase the sample size from r(n) to n (using either one of the above two imputation procedures).

Suggested Citation

  • Mojirsheibani, Majid, 2001. "The Glivenko-Cantelli theorem based on data with randomly imputed missing values," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 385-396, December.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:385-396

    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. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "Unconditional Glivenko-Cantelli-type theorems and weak laws of large numbers for bootstrap," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 365-375, March.
    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. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.


    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:stapro:v:55:y:2001:i:4:p:385-396. 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.