[R] Confidence intervals of quantiles

[mikewhite.diu at tiscali.co.uk]

Many thanks for all the contributions to this problem.
As inferred by Ted Harding, I was after a distribution-free CIs as a lot
of
the data I use is not normally distributed.

The method provided by Ted for calculating exact CIs gave good results with
the limits almost symmetric about the quantile.  Even for my smaller data
set with only 115 samples and a very skewed distribution the results clearly
showed the increase in range and asymmetry of the confidence limits.

The bootstrap method provided by Dimitris also works reasonably well but
is
slower and the ranges for the CIs are sometimes very asymmetric and in one
case did not actually encompass the quantile. The method would not work at
all with the skewed distribution of 115 samples until I reduced the quantile
range from 0.1 and 0.9 to 0.2 and 0.8  However, as Dimitris warned, you have
to be careful with this method for extreme quantiles and small samples.

I was also sent a method by Søren Merser, but this was incomplete.  This
method was written by Scott Chasalow and the full code can be found at
http://www.dpw.wau.nl/pv/pub/chasalow/S/win/ci.quantile/
The code was written for S-Plus but it worked ok for me in R.  This method
actually gives several ranges about the quantile, each with about the same
level of confidence and the level of confidence is also in the output. As
with Ted Harding's method, these may not exactly match the desired
confidence level.  There is an option to select the shortest range but it
would be easy enough to add code to give the most symmetric range.

As a chemist I am not able to comment on the statistical pros and cons of
the methods but they are certainly very helpful for my purposes.

Many thanks
Mike White

----- Original Message ----- 
From: "Dimitris Rizopoulos" <dimitris.rizopoulos at med.kuleuven.be>
To: "Mike White" <mikewhite.diu at btconnect.com>
Cc: <R-help at stat.math.ethz.ch>
Sent: Monday, February 05, 2007 2:43 PM
Subject: Re: [R] Confidence intervals of quantiles


> you could use the Bootstrap method, using package 'boot', e.g.,
>
> library(boot)
>
> f.quantile <- function(x, ind, ...){
>     quantile(x[ind], ...)
> }
>
> ###########
>
> x <- rgamma(750, 2)
> quant.boot <- boot(x, f.quantile, R = 1000, probs = c(0.025, 0.25,
> 0.5, 0.75, 0.975))
> lapply(1:5, function(i) boot.ci(quant.boot, c(0.90, 0.95), type =
> c("perc", "bca"), index = i))
>
> y <- rgamma(150, 2)
> quant.boot <- boot(y, f.quantile, R = 1000, probs = c(0.025, 0.25,
> 0.5, 0.75, 0.975))
> lapply(1:5, function(i) boot.ci(quant.boot, c(0.90, 0.95), type =
> c("perc", "bca"), index = i))
>
>
> However, you should be a little bit careful with Bootstrap if you wish
> to obtain CIs for extreme quantiles in small samples.
>
> I hope it helps.
>
> Best,
> Dimitris
>
> ----
> Dimitris Rizopoulos
> Ph.D. Student
> Biostatistical Centre
> School of Public Health
> Catholic University of Leuven
>
> Address: Kapucijnenvoer 35, Leuven, Belgium
> Tel: +32/(0)16/336899
> Fax: +32/(0)16/337015
> Web: http://med.kuleuven.be/biostat/
>      http://www.student.kuleuven.be/~m0390867/dimitris.htm
>
>
> ----- Original Message ----- 
> From: "Mike White" <mikewhite.diu at btconnect.com>
> To: <R-help at stat.math.ethz.ch>
> Sent: Monday, February 05, 2007 2:47 PM
> Subject: [R] Confidence intervals of quantiles
>
>
> > Can anyone please tell me if there is a function to calculate
> > confidence
> > intervals for the results of the quantile function.
> > Some of my data is normally distributed but some is also a squewed
> > distribution or a capped normal distribution. Some of the data sets
> > contain
> > about 700 values whereas others are smaller with about 100-150
> > values, so I
> > would like to see how the confidence intervals change for the
> > different
> > distributions and different data sizes.
> >
> > Thanks
> > Mike White
> >
> > ______________________________________________
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> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
>
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>


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