[R] ks.test()

[kjetil brinchmann halvorsen]

On 28 Aug 2003 at 8:06, Roger Koenker wrote:

But is it worth it to modify Kolmogorov-Smirnof fot estimated 
parameters? It has very low power anyhow. If the null hypothesis is 
"exponential distributio" (which is a scale family), what about using 
the quantile transformation twice

new <- qnorm(pexp(old))

to transform from exponential to normal distribution and the applying
shapiro.test
?

Kjetil Halvorsen

> 
> On Thu, 28 Aug 2003, Prof Brian Ripley wrote:
> 
> > You appear to be applying the KS test after estimating parameters.  The
> > distribution theory is for an iid sample from a known continuous
> > distribution (and does not otherwise depend on the distribution).  Since
> > your H_0 is not pre-specified, that distribution theory is not correct.
> > (Some corrections have been worked out for say ML fitting of exponential
> > and normal distributions -- by Michael Stephens as I recall.)
> 
> Just to amplify this comment a bit, I'm a little worried that the
> current documentation of of ks.test may make it appear that estimated
> parameters are ok, or that somehow the p-values computed are
> "corrected" in some way for their existence -- which I very much
> doubt.  The standard reference on this sort of thing was Durbin's (1973)
> SIAM monograph.  There is a very nice approach due to Khmaladze (1981)
> based on the Doob-Meyer decomposition - this is the closest thing
> that I'm aware of for handling KS type tests with estimated parameters
> in a general context.
> 
> url:	www.econ.uiuc.edu/~roger/my.html	Roger Koenker
> email	rkoenker at uiuc.edu			Department of Economics
> vox: 	217-333-4558				University of Illinois
> fax:   	217-244-6678				Champaign, IL 61820
> 
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