One-Sided and Two-Sided Tolerance Intervals in General Mixed and Random Effects Models Using Small-Sample Asymptotics
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of the American Statistical Association.
Volume (Year): 107 (2012)
Issue (Month): 497 (March)
Contact details of provider:
Web page: http://www.amstat.org/publications/jasa/index.cfm?fuseaction=main
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Michael McNulty).
If references are entirely missing, you can add them using this form.