If you compute the observed information for sigma from a sample of size 1 from a N(0,sigma^2) distribution, you will find that the observed information can be negative definite with a high probability. So it can happen!
Cheers! John Holt ----------------------------------------------------- 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 ----------------------------------------------------- John Holt, Ph.D. Dept. Mathematics and Statistics University of Guelph Guelph, ON N1G 2W1 Tel 519-824-4120Ext53297/52155 ______________________________________________ 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
