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Re: st: parametric vs. nonparametric estimators

From   Roger Newson <>
Subject   Re: st: parametric vs. nonparametric estimators
Date   Wed, 16 Jun 2004 19:23:56 +0100

At 18:52 16/06/2004, Thomas wrote:
Dear Nick and Rich,

maybe I miss something, but my problem is as follows:

suppose I have a data set with 100 objects and two binary variables, X
(sex=male (coded 1) or female (coded 0)) and Y (disease=absent (coded 0) or
present (coded 1)) for example. My goal is to estimate the probability
P(Y=1|X=1). Suppose 50 of the 100 persons are male and of this 10 have a
disease, then my so called "nonparametric" estimate of P(Y=1|X=1) is
10/50=0.200. By nonparametric I mean, that no assumption about the
distribution of Y is made. By using logistic regression, I assume that Y can
be related to a latent variable Y* which has a logistic distribution. Now,
for example, the logistic regression estimate of P(Y=1|X=1) is 0.201. What
does the difference between 0.200 and 0.201 tell me?
Probably not a great deal. A difference of half a percent in fitted value could easily be due to imperfect numerical precision during an iterative fit, which your "parametric" estimate uses and your "nonparametric" model doesn't.


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
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