RE: [R] (Off topic.) Observed Fisher information.

From: Ravi Varadhan <rvaradha_at_jhsph.edu>
Date: Tue 07 Jun 2005 - 09:25:07 EST


Hi Rolf,

If your data come from exponential family of distributions, then the log-likelihood is concave and the observed information must be positive definite. However, I don't think that this is the case more generally, i.e. for families such as curved exponential families the log-likelihood doesn't have to concave. I remember reading something about this in Barndorff-Nielsen and Cox's book on Inference and Asymptotics. There may be better references.

Ravi.



Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan@jhmi.edu

> -----Original Message-----
> From: r-help-bounces@stat.math.ethz.ch [mailto:r-help-
> bounces@stat.math.ethz.ch] On Behalf Of Rolf Turner
> Sent: Monday, June 06, 2005 6:49 PM
> To: r-help@stat.math.ethz.ch
> Subject: [R] (Off topic.) Observed Fisher information.
>
> I have been building an R function to calculate the ***observed***
> (as opposed to expected) Fisher information matrix for parameter
> estimates in a rather complicated setting. I thought I had it
> working, but I am getting a result which is not positive definite.
> (One negative eigenvalue. Out of 10.)
>
> Is it the case that the observed Fisher information must be positive
> definite --- thereby indicating for certain that there are errors in
> my code --- or is it possible for such a matrix not to be pos. def.?
>
> It seems to me that if the log likelihood surface is ***not*** well
> approximated by a quadratic in a neighbourhood of the maximum, then
> it might well be that case that the observed information could fail
> to be positive definite. Is this known/understood? Can anyone point
> me to appropriate places in the literature?
>
> TIA.
> cheers,
>
> Rolf Turner
>
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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jun 07 09:29:18 2005

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