[R] ks.test()

Roger Koenker roger at ysidro.econ.uiuc.edu
Thu Aug 28 15:06:54 CEST 2003

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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