[19137] in s-news-athena
[S] Summary Error propagation
daemon@ATHENA.MIT.EDU (Ekkehardt Altpeter)
Wed Sep 8 04:54:48 1999
Date: Wed, 08 Sep 1999 10:40:09 +0200
From: Ekkehardt Altpeter <altpeter@ispm.unibe.ch>
To: s-news@wubios.wustl.edu
Message-Id: <3.0.1.32.19990908104009.0091ae60@karajan.unibe.ch>
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Dear S community,
here is the answer from Prof. B. Ripley and it works as it should.
Sincerely,
Ekkehardt Altpeter
>
> Dear S+ specialists,
>
> I have a mathematical problem to solve and can't find a proper solution:
>
> given a function B=f(b,c) under the assumption that ~N(c(b,c),var(b,c)),
> where b and c are the maximum liklihood estimates of b and c (or estimates
> of an M-estimation), find the estimate of variance var(B).
In general you can't do this exactly analytically. The usual approximation
is called the Delta Method (bug name for a small idea): replace f
by the tangent plane (= first-order Taylor expansion) at mean of b and c
(you seem to have two meanings of b and three of c). You can easily
compute the variance of a linear function.
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