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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 19:52:13 +0200 |

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? I hope things are now more clear! Thanks for your time and effort! Thomas -----Ursprüngliche Nachricht----- Von: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]Im Auftrag von Nick Cox Gesendet: Mittwoch, 16. Juni 2004 17:25 An: statalist@hsphsun2.harvard.edu Betreff: RE: st: parametric vs. nonparametric estimators This sounds like a thread letting Theseus (or the thesis) escape from a semantic maze, but it hinges on one notion of a parameter. Thus even with Wilcoxon-Mann-Whitney and only minimal assumptions (continuity?) about what kind of distributions are being postulated, the common U statistic can be scaled to give an estimate of pr(X > Y). Indeed Rich was one of the people instrumental in getting StataCorp to add the -porder- option to -ranksum-. I'd want to regard this probability as a parameter (property of the system or chance set-up which can be estimated) and an estimate of it is sometimes more interesting or useful than the U statistic or its P-value. It's perhaps then just that it is not a parameter which specifies a probability distribution (i.e. distribution, mass or density function). (Roger Newson would want me to point out that this pr(X > Y) is just Somers' d in one of its many guises. Shall I compare thee to a Somers' d? (Shakespeare)) Nick n.j.cox@durham.ac.uk Richard Goldstein > I'm a little confused about what you mean by a parameter estimated > via non-parametric methods; to me, non-parametric means that no > parameter is estimated (yes, I distinguish between non-parametric > and "distribution free") * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: parametric vs. nonparametric estimators***From:*Roger Newson <roger.newson@kcl.ac.uk>

**References**:**RE: st: parametric vs. nonparametric estimators***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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