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
[email protected]
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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