From: Alan Arnholt <arnholt_at_cs.cs.appstate.edu>

Date: Fri 30 Dec 2005 - 05:41:10 EST

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 Received on Fri Dec 30 05:52:08 2005

Date: Fri 30 Dec 2005 - 05:41:10 EST

To my understanding, a confidence interval typically covers a single valued parameter. In contrast, a confidence band covers an entire line with a band. In regression, it is quite common to construct confidence and prediction bands. I have found that many people are connecting individual confidence/prediction interval values produced with predict(object,sd.fit=T,type="conf/pred") and calling the result a confidence/prediction band. Since there is no specific probability statement that can be attached to these connected confidence/prediction intervals, this does not seem reasonable to me. This is done, for example, in ISWR pg. 105, UsingR for Introductory Statistics pg 296, and Linear Models with R pg. 39 (Although in this instance the intervals are called 95% "pointwise" confidence bands versus simply 95% confidence bands.) To make a confidence/prediction band, one should construct simultaneous confidence/prediction intervals with say a Scheffe approach as mentioned in the S-PLUS Guide to statistics pg 274. If these connected intervals were called pointwise confidence/prediction intervals with the understanding that have no particular probability interpretation, then they are useful in understanding where the line should fall. However, they are not confidence/prediction bands as such, and I think it is misleading to name them so. Should the intervals the authors in the three mentioned references construct not be called something similar to connected 95% pointwise confidence/prediction intervals versus 95% confidence/prediction bands? Or, have I missed the boat? Fire away...

Alan T. Arnholt

Associate Professor

Dept. of Mathematical Sciences

Appalachian State University

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 Received on Fri Dec 30 05:52:08 2005

*
This archive was generated by hypermail 2.1.8
: Fri 03 Mar 2006 - 03:41:44 EST
*