From: Berton Gunter <gunter.berton_at_gene.com>

Date: Mon 18 Sep 2006 - 16:28:24 GMT

R-help@stat.math.ethz.ch 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. Received on Tue Sep 19 02:34:12 2006

Date: Mon 18 Sep 2006 - 16:28:24 GMT

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

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