[R] Goodness of fit test for estimated distribution

[Spencer Graves]

      What about Monte Carlo?  I recently produced (with help from 
contributors to this list) qq plots for certain complicated mixtures of 
distributions.  To evaluate goodness of fit, I produced Monte Carlo 
confidence intervals from 401 simulated qq plots and took the 11th and 
391st of them for each quantile.  {quantile(1:401, c(.025, .975)) = 
c(11, 391)}.  Something like this could be done to obtain a significance 
level for ks.test, for example. 

      This may not be as satisfying for some purposes as a clean, 
theoretical result, but it produced useful answers without busting the 
project budget too badly. 

      hope this helps. 
      spencer graves

roger koenker wrote:

> In full generality this is a quite difficult problem as discussed in
> Durbin's (1973) SIAM monograph.  An elegant general approach
> is provided by Khmaladze
>
> @article{Khma:Arie:1981,
>     author = {Khmaladze, E. V.},
>     title = {Martingale approach in the theory of goodness-of-fit tests},
>     year = {1981},
>     journal = {Theory of Probability and its Applications (Transl of 
> Teorija Verojatnostei i ee Primenenija)},
>     volume = {26},
>     pages = {240--257}
> }
>
> but I don't think that there is a general implementation of the 
> approach for R, or
> any other software environment, for that matter.
>
> url:    www.econ.uiuc.edu/~roger            Roger Koenker
> email    rkoenker at uiuc.edu            Department of Economics
> vox:     217-333-4558                University of Illinois
> fax:       217-244-6678                Champaign, IL 61820
>
> On Jun 29, 2004, at 1:08 PM, Christian Hennig wrote:
>
>> Hi,
>>
>> is there any method for goodness of fit testing of an (as general as
>> possible) univariate distribution with parameters estimated, for normal,
>> exponential, gamma distributions, say (e.g. the corrected p-values for
>> the Kolmogorov-Smirnov or Chi-squared with corresponding ML estimation
>> method)?
>> It seems that neither ks.test nor chisq.test handle estimated 
>> parameters.
>> I am aware of function goodfit in package vcd, which seems to it for 
>> some
>> discrete distributions.
>>
>> Thank you for help,
>> Christian
>>
>>
>> ***********************************************************************
>> Christian Hennig
>> Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
>> hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
>> #######################################################################
>> ich empfehle www.boag-online.de
>>
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