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RE: st: parametric vs. nonparametric estimators


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: parametric vs. nonparametric estimators
Date   Wed, 16 Jun 2004 16:24:47 +0100

This sounds like a thread letting Theseus (or the 
thesis) escape from a semantic maze, 
but it hinges on one notion of a parameter. 

Thus even with Wilcoxon-Mann-Whitney 
and only minimal assumptions (continuity?) about what 
kind of distributions are being postulated, the 
common U statistic can be scaled to give an 
estimate of pr(X > Y). Indeed Rich was one of
the people instrumental in getting StataCorp 
to add the -porder- option to -ranksum-. I'd 
want to regard this probability as a parameter
(property of the system or chance set-up which 
can be estimated) and an estimate of it is sometimes
more interesting or useful than the U statistic or 
its P-value. It's perhaps then just that
it is not a parameter which specifies a probability 
distribution (i.e. distribution, mass or density 
function). 

(Roger Newson would want me to point out that this 
pr(X > Y) is just Somers' d in one of its many 
guises. Shall I compare thee to a Somers' d? 
(Shakespeare)) 

Nick 
n.j.cox@durham.ac.uk 

Richard Goldstein
 
> I'm a little confused about what you mean by a parameter estimated
> via non-parametric methods; to me, non-parametric means that no
> parameter is estimated (yes, I distinguish between non-parametric
> and "distribution free")

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