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st: RE: RE: RE: distribution of the kernel density


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: distribution of the kernel density
Date   Mon, 9 Sep 2002 19:37:02 +0100

Lee Sieswerda <Lee.Sieswerda@tbdhu.com>

> Nick is bang on about the unsuitability (non-suitability?
anti-suitability?)
> of testing the kernel density for the purposes of making conclusions
about
> the original variable. After all, the kernel density is a
mathematical
> construct based on a host of assumptions that determine its form.
Clearly,
> to suppose that a test of normality on the values of the kernel
density
> would have much to say substantively on the subject of the normality
of the
> original variable would be erroneous. But, suppose, as I do, that
> Alejandro's reason for testing the kernel density isn't to make
conclusions
> about the normality of the original variable, but wants to determine
how
> close the kernel density approaches the normal distribution. Then,
wouldn't
> he be able to gather some useful information from -qnorm-
and -sktest-?

Alejandro can -- indeed should -- answer for himself, but I doubt that
this
is what he wanted. If it is, then -qnorm- might be useful graphically,
but for any significance testing, there are further difficulties
beyond
those I mentioned.

What is the sample size? The number of original values, or the number
of
points at which the density is estimated? Even more fundamentally, the
estimates of the density are themselves not independent, as in
practice to
be useful the kernels around each data point must overlap. That alone
would seem to invalidate any P-values from (say) -sktest-.

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

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