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

[Ravi Varadhan]

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 at jhmi.edu
--------------------------------------------------------------------------
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
> bounces at stat.math.ethz.ch] On Behalf Of Rolf Turner
> Sent: Monday, June 06, 2005 6:49 PM
> To: r-help at 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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-
> guide.html