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

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