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: [EMAIL PROTECTED] -------------------------------------------------------------------------- > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:r-help- > [EMAIL PROTECTED] 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 > > ______________________________________________ > R-help@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 ______________________________________________ R-help@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
