What's the current best wisdom on how to construct confidence
bounds on something like a normal probability plot?
I recall having read a suggestion to Monte Carlo something like
201 simulated lines with the same number of points, then sort the order
statistics, and plot the 6th and 196th of these. [I use 201 not 200
because quantile(1:201, c(0.025, 0.975)) = 6 and 196 while
quantile(1:200, c(0.025, 0.975)) = 5.975 and 11.025.] I think I know
how to do this, but before I code it, I'd like to ask two questions on
this issue:
1. Where can I find this in the literature? I didn't find it
where I thought it was, nor in anyplace else that seemed obvious to me,
but I don't think I made it up and I'd like to give credit where credit
it due.
2. Are there better alternatives available, especially if the
distribution is a compound mixture that is easily simulated but not so
easily characterized analytically?
Thanks,
spencer graves
Spencer Graves wrote:> What's the current best wisdom on how to construct confidence > bounds on something like a normal probability plot? > I recall having read a suggestion to Monte Carlo something like 201 > simulated lines with the same number of points, then sort the order > statistics, and plot the 6th and 196th of these. [I use 201 not 200 > because quantile(1:201, c(0.025, 0.975)) = 6 and 196 while > quantile(1:200, c(0.025, 0.975)) = 5.975 and 11.025.] I think I know > how to do this, but before I code it, I'd like to ask two questions on > this issue: > 1. Where can I find this in the literature? I didn't find it > where I thought it was, nor in anyplace else that seemed obvious to me, > but I don't think I made it up and I'd like to give credit where credit > it due. > 2. Are there better alternatives available, especially if the > distribution is a compound mixture that is easily simulated but not so > easily characterized analytically? > Thanks, > spencer graves > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.htmlJohn Fox has qq.plot() in his "car" package for (not only) plotting pointwise confidence envelops into QQ-Plots. See his books: @BOOK{fox:1997, author = "Fox,~J.", title= {{Applied Regression Analysis, Linear Models, and Related Methods}}, publisher = {Sage}, address = "Thousand Oaks", year = "1997" } @BOOK{fox:2002, author = "Fox,~J.", title= {{An R and S-PLUS Companion to Applied Regression}}, publisher = {Sage}, address = "Thousand Oaks", year = "2002" } Uwe Ligges
Dr. Venables used that as an example for program efficiency in his Advanced S-PLUS programming course, which I took a few years back. He cited Atkinson (1985). Unfortunately I do not have my copy of Atkinson on hand... Best, Andy> From: Spencer Graves > > What's the current best wisdom on how to construct confidence > bounds on something like a normal probability plot? > > I recall having read a suggestion to Monte Carlo something like > 201 simulated lines with the same number of points, then sort > the order > statistics, and plot the 6th and 196th of these. [I use 201 not 200 > because quantile(1:201, c(0.025, 0.975)) = 6 and 196 while > quantile(1:200, c(0.025, 0.975)) = 5.975 and 11.025.] I think I know > how to do this, but before I code it, I'd like to ask two > questions on > this issue: > > 1. Where can I find this in the literature? I didn't find it > where I thought it was, nor in anyplace else that seemed > obvious to me, > but I don't think I made it up and I'd like to give credit > where credit > it due. > > 2. Are there better alternatives available, especially if the > distribution is a compound mixture that is easily simulated > but not so > easily characterized analytically? > > Thanks, > spencer graves > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >
Spencer, Venables & Ripley's S Programming (2000) book comprehensively covers "Simulation envelopes for normal scores plots" in Section 7.3, pages 161 - 163. The Atkinson "Plots, Transformations, and Regression" (1985) book is cited. The V & R example and discussion, as usual, is very informative on both the programming and data analysis fronts. Hope that helps, Bill ---------------------------------------- Bill Pikounis, Ph.D. Biometrics Research Department Merck Research Laboratories> -----Original Message----- > From: r-help-bounces at stat.math.ethz.ch > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves > Sent: Tuesday, June 01, 2004 2:36 PM > To: R Help > Subject: [R] Confidence Bounds on QQ Plots? > > > What's the current best wisdom on how to construct confidence > bounds on something like a normal probability plot? > > I recall having read a suggestion to Monte Carlo something like > 201 simulated lines with the same number of points, then sort > the order > statistics, and plot the 6th and 196th of these. [I use 201 not 200 > because quantile(1:201, c(0.025, 0.975)) = 6 and 196 while > quantile(1:200, c(0.025, 0.975)) = 5.975 and 11.025.] I think I know > how to do this, but before I code it, I'd like to ask two > questions on > this issue: > > 1. Where can I find this in the literature? I didn't find it > where I thought it was, nor in anyplace else that seemed > obvious to me, > but I don't think I made it up and I'd like to give credit > where credit > it due. > > 2. Are there better alternatives available, especially if the > distribution is a compound mixture that is easily simulated > but not so > easily characterized analytically? > > Thanks, > spencer graves > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >