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st: 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: distribution of the kernel density
Date   Mon, 9 Sep 2002 14:23:34 +0100

Alejandro Riano  

> > Someone knows if there is an statistic which I could use 
> to asses if the
> > kernel density for a given variable follows a normal 
> distribution ?

Lee Sieswerda
> 
> How about:
> kdensity var1, gen(x y)
> qnorm y
> sktest y

The second variable which -kdensity- generates 
is a density, which is not a suitable input 
for -qnorm- or -sktest-. 

Setting that aside, passing 
data through a kernel density estimation 
command can add no information suitable 
for _any_ formal test of normality or 
non-normality, and at best it obscures 
the testing issue. To see this, note that 
if you choose a Gaussian kernel and 
increase its width, inevitably the 
"estimated" distribution approaches Gaussian 
form. More generally, any test would depend 
on which kernel you choose 
and on its width as much as on the 
sample data, which makes no sense. 

I support Lee's notion of using -qnorm-, but 
on the original data. Another plot 
which deserves a brief experiment 
is -dpplot- on SSC. 

For reasons often rehearsed on 
this list, -swilk-, -sfrancia- 
and -sktest- are in practice almost 
always less illuminating than graphs. 

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