IDEAS home Printed from
   My bibliography  Save this article

One-Sided and Two-Sided Tolerance Intervals in General Mixed and Random Effects Models Using Small-Sample Asymptotics


  • Gaurav Sharma
  • Thomas Mathew


The computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and/or when covariates are present. This article derives satisfactory one-sided and two-sided tolerance intervals in such a general scenario, by applying small-sample asymptotic procedures. In the case of one-sided tolerance limits, the problem reduces to the interval estimation of a percentile, and accurate confidence limits are derived using small-sample asymptotics. In the case of a two-sided tolerance interval, the problem does not reduce to an interval estimation problem; however, it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components. For the latter problem, small-sample asymptotic procedures can once again be used to arrive at an accurate upper confidence limit. In the article, balanced and unbalanced data situations are treated separately, and computational issues are addressed in detail. Extensive numerical results show that the tolerance intervals derived based on small-sample asymptotics exhibit satisfactory performance regardless of the sample size. The results are illustrated using some examples. Some technical derivations, additional simulation results, and R codes are available online as supplementary materials.

Suggested Citation

  • Gaurav Sharma & Thomas Mathew, 2012. "One-Sided and Two-Sided Tolerance Intervals in General Mixed and Random Effects Models Using Small-Sample Asymptotics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 258-267, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:258-267
    DOI: 10.1080/01621459.2011.640592

    Download full text from publisher

    File URL:
    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.

    More about this item


    Access and download statistics


    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:taf:jnlasa:v:107:y:2012:i:497:p:258-267. 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: (Chris Longhurst). 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.

    We have no 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.

    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.