[RsR] minimum sample size for the robust counterpart of the t-test

[Martin Maechler]

>>>>> Richard Friedman <friedman using cancercenter.columbia.edu>
>>>>>     on Wed, 15 Jun 2011 15:10:03 -0400 writes:

    > Dear List, I am a beginner in the use of robust methods. Is
    > there a minimum sample size for which the robust analog of a two
    > sample t-test using rlm with default parameters and categorical
    > explanatory variables may be trusted to yield reliable p-values?
    > Is so, can you please point me at a reference which treats this
    > problem.

It's a bit more complicated, because "the" robust analog does
not exist:  There are an infinite number of possible robust
analogues to the t-test,
and my two colleagues have been actively researching on this,
not just for the two-sample case, but the general  lm() case,
*with* an emphasis on small-sample performance:

Originally, (I think) they started answering the question (+/-): 

  How do you have to estimate  sj^2 := \Var(\hat{\beta_j}) such that
    \hat{\beta_j}  +/- 1.96 * sj
  has the correct coverage probability of 95%, also for small
  samples (and of course generalizing to other probs. alpha).
 
Here's their main publication :     

 Koller, M. and Stahel, W.A. (2011), Sharpening Wald-type inference
 in robust regression for small samples, _Computational Statistics
 & Data Analysis_ *55*(8), 2504-2515.

and the good news is that Manuel Koller has implemented
everything in package robustbase, lmrob() {which you'd use
instead of rlm()},
and to use the new methods, you use (something like)

   summary( fmod <- lmrob(Y ~ ., data=..., setting = 'KS2011') )

I've CC'ed them here, just in case they are accidentally not yet
subscribed to the R-SIG-Robust mailing list.

I hope this helps,
Martin Maechler, ETH Zurich


    > Thanks and best wishes, Rich
    > ------------------------------------------------------------
    > Richard A. Friedman, PhD Associate Research Scientist,
    ................
    ................

    > R-SIG-Robust using r-project.org mailing list
    > https://stat.ethz.ch/mailman/listinfo/r-sig-robust