R help - Nov 2005 - Permutation tests for correlations

Apropos the question about permutation tests in multiple regression:

We do have perm.test in package ExactRankTests, but it does one- and
two-sample tests, as in t.test, wilcox.test, etc. There doesn't seem
to be an exact version of the permutation test for correlations, i.e.,
the one that could be estimated using

replicate(10000, cor(x,sample(y))) # or other values of 10000

or, of course, computed exactly by enumeration of all the
permutations, which is feasible up to length(x) == 10 or so.

So I'm wondering: Is this due to lack of theory/algorithm or just lack of
implementation? 

-- 
   O__  ---- Peter Dalgaard             ??ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

On Wed, 30 Nov 2005, Peter Dalgaard wrote:
> Apropos the question about permutation tests in multiple regression:
>
> We do have perm.test in package ExactRankTests, but it does one- and
just for the record: exactRankTests.
> two-sample tests, as in t.test, wilcox.test, etc. There doesn't seem
> to be an exact version of the permutation test for correlations, i.e.,
> the one that could be estimated using
>
> replicate(10000, cor(x,sample(y))) # or other values of 10000
>
> or, of course, computed exactly by enumeration of all the
> permutations, which is feasible up to length(x) == 10 or so.
>
> So I'm wondering: Is this due to lack of theory/algorithm or just lack
of
> implementation?
Lack of looking at the right package ;-)

The package `coin' provides conditional inference for the independence
problem in a rather flexible setup (in particular for arbitrary scales of
x  and y). It provides asymptotic p values as well as approximations (as
you suggest above) to the exact distribution for all types of data and
also the exact distribution if feasible. See
  vignette("coin", package = "coin")
for more details.

Best,
Z