[R] Confidence Interval

[Bill.Venables at csiro.au]

Sorry, but the paper is wrong, or at least the language is very loose.
It does speak about a 'confidence interval' for a statistic, but that
makes no sense.  The author apparently means a confidence interval for
the parameter for which the statistic is an estimate, and nominates the
profile likelihood interval.  This starts to make some sense.

Profile likelihood intervals are often calculated using R, but require
the low-level optimisation tools to do it.  It's easy enough, but there
is no magic button to push to get them.  At best it gets fiddly.  (Some
standard problems are supported with R software, such as mixed effect
models, non-linear regressin and generalized linear models, but not this
one.)

In this game there is no way around formulating your problem very
carefully and if you want to communicate with others about it you really
need to use the language in a careful, even pedantic way.  The territory
comes with many bear traps and quicksand pits.

Bill Venables.

-----Original Message-----
From: Jacques Wagnor [mailto:jacques.wagnor at gmail.com] 
Sent: Monday, 4 February 2008 12:59 PM
To: Venables, Bill (CMIS, Cleveland)
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] Confidence Interval

The motivation for the question comes from Figure 3 of this paper
http://www.ma.hw.ac.uk/~mcneil/ftp/cad.pdf, which shows that a
confidence interval for a statistic is possible.  Does there exist a
function in R for such a calculation?  If not, how would one go about
doing it in R?

Any pointers would be greatly appreciated.

On Feb 3, 2008 12:21 AM,  <Bill.Venables at csiro.au> wrote:
> Your question is not clear.  Confidence intervals apply to parameters.
> What you set out below is a simulation strategy.  x is a simulated
> sample and y is a statistic based on it.  There is no 'model' in any
> statistical sense.
>
> What is the parameter for which you want a confidence interval?
>
> What data set, or sets, will you have available to do it?
>
> Do you want to make parametric assumptions (in which case the
Likelihood
> Ratio interval may be possible) or do you want to use a non-parametric
> interval, keeping the assumptions as weak as possible (in which case,
> inverting the sign test might be appropriate)?
>
> Finally, what has this got to do with R-help?
>
>
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org]
> On Behalf Of Jacques Wagnor
> Sent: Sunday, 3 February 2008 12:42 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Confidence Interval
>
> I have a model as follows:
>
> x <- replicate(100, sum(rlnorm(rpois(1,5), 0,1)))
> y <- quantile(x, 0.99)
>
> How would one go about estimating the boundaries of a 95% confidence
> interval for y?
>
> Any pointers would be greatly appreciated.
>
> > version
> _
> platform i386-pc-mingw32
> arch i386
> os mingw32
> system i386, mingw32
> status
> major 2
> minor 5.1
> year 2007
> month 06
> day 27
> svn rev 42083
> language R
> version.string R version 2.5.1 (2007-06-27)
>
> Jacques
>
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>
>