[R] a Bootstrap understanding problem

[Prof Brian Ripley]

On Mon, 21 Jan 2002, Wilhelm B. Kloke wrote:

> I tried to reproduce a result from a former colleague which he got
> with S-plus bootstrap method. I don't have S-plus at hand.
>
> In R, there are 2 packages related to bootstrap method, bootstrap and
> boot. The former has a function called 'bootstrap' but this does not
> seem to conform either to the function used in S-plus nor to that
> described in MASS, 3d ed., p.144.

It certainly does not conform.  The `bootstrap' package (its original S
name was bootstrap.funs) is old and I suggest should not now be used, but
it does have a function for BCa which you could find by looking in its
INDEX.  The example is even

     # For example, find bca limits for
     # the correlation coefficient from a set of 15 data pairs:

but the bootstrap set is tiny (see below).

> The latter seems to be applicable to the problem I have been asked for
> help, but I am not happy insofar, as the BCa percentile confidence
> interval
> I am getting now is a lot larger. (The data I want to estimate are
> correlations of 13 data pairs. The lower ci bound went from about 0.16
> to
> 0.03 for the same data set.)
>
> Is there a known difference in the use of the wording BCa percentile?

No, and in e.g. the MASS examples they give similar results.

BCa needs large, often very large (tens of thousands), bootstrap sets.
Are you sure your colleague used a large enough set?  A quick bit of
replication suggests that the BCa limits are very variable for your
problem. I find BCa pretty unreliable, and for correlations using Fisher's
tanh transformation is normally enough to make all sensible confidence
interval procedures agree for all practical purposes.

Finally, what useful conclusions can be drawn from a confidence interval
for the correlation of 13 data pairs?

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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