Rich Ulrich wrote:
> - In my vocabulary, these days, "nonparametric" starts out with data
> being ranked, or otherwise being placed into categories -- it is the
> infinite parameters involved in that sort of non-reversible re-scoring
> which earns the label, nonparametric. (I am still trying to get my
> definition to be complete and concise.)
Well, I am happy for you to use this definition of nonparametric now
that you've said what you want it to mean, but it isn't exactly
what most statisticians - including those of us that distinguish
between the terms "distribution-free" and "nonparametric" - mean
by "nonparametric", so you'll have to excuse my earlier ignorance
of your definition.
If my recollection is correct, a parametric procedure is where the
entire distribution is specified up to a finite number of parameters,
whereas a nonparametric procedure is one where the distribution
can't be/isn't specified with only a finite number of unspecified
parameters. This typically includes the usual distribution-free
procedures, including many rank-based procedures, but it also
includes many other things - including some that don't transform
the data in any way, and even some based on means.
So, for example, ordinary simple linear regression is parametric,
because the distribution of y|x is specified, up to the value of
the parameters specifying the intercept and slope of the line, and
the variance about the line.
Nonparametric regression (as the term is typically
used in the literature), by contrast, is effectively
infinite-parametric, because the distribution of y|x
doesn't depend only on a finite number of parameters
(often the distribution *about* E[y|x] is parametric
- typically gaussian - but E[y|x] itself is where the
infinite-parametric part comes from).
Nonparametric regression would not seem to fit your definition
of "nonparametric", since your usage seems to require some
loss of information through ranking or categorisation.
Once we start using the same terminology, we tend to find the
disagreements die down a bit.
Glen
