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AW: st: parametric vs. nonparametric estimators


From   Thomas Mählmann <maehlmann@wiso.uni-koeln.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   AW: st: parametric vs. nonparametric estimators
Date   Wed, 16 Jun 2004 09:43:25 +0200

Dear Roger,

to be more concrete, I have a data set with a binary variable (1=disease)
and I want the estimate  the disease probability for different subsets of
the population (e.g. age, sex etc.). My nonparametric estimator is simply
the disease proportion and the parametric estimate is based on logistic
regression. Standard errors are estimated via bootstap.

Thomas

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]Im Auftrag von Roger Newson
Gesendet: Dienstag, 15. Juni 2004 21:18
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: parametric vs. nonparametric estimators


At 19:11 15/06/2004, Thomas wrote:
>Dear Statalisters,
>
>this is rather a general statistic than a Stata related question, but
>nevertheless I hope someone can give me some help.
>
>I have estimated a population parameter using both a nonparametric and a
>parametric estimator. To my surprise both approaches yield about the same
>point estimates, but the parametric estimator has a somewhat lower standard
>error.
>
>Do these results imply that the model assumptions underlying the parametric
>estimator are correct?

You do not specify your example a great deal. However, in general, the
answer is no. Sometimes, erroneous assumptions make the standard error
unrealistically low.

A textbook example would be the use of the equal-variance t-test when the
smaller of 2 samples is from a much more variable population than the
larger of 2 samples. THe equal-variance t-test assumes that you can
estimate the population variance of the smaller sample using the sample
variance of the larger sample. This will produce unrealistically low
standard errors for the difference between means, if the population
variance of the smaller sample is a lot larger than the population variance
of the larger sample.

I hope this helps.

Best wishes

Roger


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
   or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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