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Re: st: parametric vs. nonparametric estimators


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: parametric vs. nonparametric estimators
Date   Tue, 15 Jun 2004 20:17:57 +0100

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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