[R] coin package (conditional inference / permutation): parameter teststat

[Paulo Barata]

Dear R-list members,

This is in fact a question about statistics, not directly
about the R software.

The coin package, for conditional inference through permutation
methods, has as it main function the function  independence_test.
One of its parameters is teststat, about which the package
documentation says:

  teststat: "a character, the type of test statistic to be applied:
  either a standardized scalar test statistic (scalar), or
  a maximum type statistic (max) or a quadratic form (quad).

My current problem is a two-sample (two-group) one, with
multivariate response consisting entirely of continuous numerical
observations.

Would someone please point me to references indicating the relative
merits of the "max" and "quad" test statistics in this case?

The pdf document "Implementing a Class of Permutation Tests: The
coin Package", by Hothorn et al., which comes with the package,
says on page 5 that "In the multivariate case (pq > 1),
a maximum-type statistic (...) is appropriate". But no reasons
or references are provided.

P. Good, Permutation, Parametric, and Bootstrap Tests of Hypotheses.
3rd. ed. (Springer), says on page 180 (Section 9.4.4, Which
Statistic?) [my comments in brackets]:

  "We've now considered three multivariate test statistics for
  testing hypothesis based on one or two samples. Which one should
  we use? To detect a simultaneous shift in the means of several
  variables, use Hotelling's T2 [a kind of 'quad' test statistics];
  to detect a shift in any of several variables, use the maximum t
  [a kind of 'max' test statistics] (...)"

But again, no reasons or references are provided.

So, I would like to know if anyone could indicate me references
discussing the relative merits of the "max" and "quad" test
statistics, in the case of a two-sample problem with continuous
multivariate responses, when using permutation tests.

Just for information, I currently use R 2.7.1 running on
Windows XP. The coin package is version 0.6-9 (5 May 2008).

Thank you very much.

Regards,

Paulo Barata

-----------------------------------------------------------------------
Paulo Barata
Fundacao Oswaldo Cruz
Rua Leopoldo Bulhoes 1480 - 8A
21041-210  Rio de Janeiro - RJ
Brazil

E-mail: pbarata at infolink.com.br
Alternative e-mail: paulo.barata at ensp.fiocruz.br