Berton, Thanks for your inupt. The 'nist' link you mentioned was one of the reasons for my confusion and how it is implemented in R. As for now I am assuming predict function with 'prediction' option will provide me tolerance/prediction interval. Is this a proper assumption? TIA for your help. Sachin
Berton Gunter <[EMAIL PROTECTED]> wrote: Peter et. al.: > > With those definitions (which are hardly universal), tolerance > intervals are the same as prediction intervals with k == m == 1, which > is what R provides. > > I don't believe this is the case. See also: http://www.itl.nist.gov/div898/handbook/prc/section2/prc263.htm This **is** fairly standard, I believe. For example, see the venerable classic text (INTRO TO MATH STAT) by Hogg and Craig. To be clear, since I may also be misinterpreting, what I understand/mean is: Peter's definition of a "tolerance/prediction interval" is a random interval that with a prespecified confidence contain a future predicted value; The definition I understand to be a random interval that with a prespecified confidence will contain a prespecfied proportion of the distribution of future values. ..e.g. a "95%/90%" tolerance interval will with 95% confidence contain 90% of future values (and one may well ask, "which 90%"?). Whether this is a useful idea is another issue: the parametric version is extremely sensitive (as one might imagine) to the assumption of exact normality; the nonparametric version relies on order statistics and is more robust. I believe it is nontrivial and perhaps ambiguous to extend the concept from the usual fixed distribution to the linear regression case. I seem to recall some papers on this, perhaps in JASA, in the past few years. As always, I welcome correction of any errors or misunderstandings herein. Cheers to all, Bert Gunter --------------------------------- [[alternative HTML version deleted]] ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
