Talk:Confidence and prediction bands

What are "simultaneous 95% confidence bands"

I don't understand "simultaneous 95% confidence bands". The standard 95% confidence bands around a regression line include the true but unknown line in 95 percent of regressions. This article seems mostly about simultaneous confidence bands, without adequate explanation of the circumstances under which one would want to use them over the traditional confidence bands, herein described as "pointwise". It needs a persuasive example where one would clearly want "simultaneous" bands. The "pointwise" bands are much more commonly used, in my experience, and I think this article needs a discussion of them.

Also, I would think that any discussion of "simultaneous" intervals should explain how they relate or don't to tolerance intervals, at least some of which require two probabilities, not one

And I'm not convinced that Scheffé's method is relevant here: The Wikipedia article on Scheffé's method says it is used to compare "the means of some variable in r disjoint populations." This article on "Confidence and prediction bands" does not have "r disjoint populations." I'm confused.

I find the section on "Pointwise and simultaneous confidence bands" less than persuasive: If the function f(x) is continuous, then it can be defined at infinitely many points within the range of the data. In such cases, it would seem to me that "r" for Scheffé's method would be infinite, which would in turn would require using an F with denominator degrees of freedom being negative infinite. I must be missing something.

I came here looking for a plot showing prediction intervals about regression -- preferably both confidence and prediction intervals about a given regression. I didn't find one. This article should have one, I think. These standard (pointwise) intervals are far more widely used than any "simultaneous" bounds, I believe.

Apparently, simultaneous confidence intervals may not be as rare as I expected, because "sos::findFn('simultaneous confidence interval')" in R (programming language) identified 320 links in 115 packages on 2016-05-18, and some of these help pages related to regression. DavidMCEddy (talk) 22:48, 18 May 2016 (UTC)[reply]

@DavidMCEddy:, It's a good distinction to have because when comparing CDFs, simultaneous bands are the standard band, not pointwise. for example Dvoretzky–Kiefer–Wolfowitz_inequality gives a 95% chance that the ENTIRE empirical distribution is contained within the band. When looking at a Pointwise line, it's as if you didn't care about any other point on the line and were only trying to build a 95% confidence around a single part of your regression line. Bscan (talk) 19:26, 20 April 2018 (UTC)[reply]

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