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

From: John D. Holt <>
Date: Tue 07 Jun 2005 - 12:08:49 EST

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!

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?


Rolf Turner

John Holt, Ph.D.
Dept. Mathematics and Statistics
University of Guelph
Guelph, ON
N1G 2W1

Tel 519-824-4120Ext53297/52155 mailing list PLEASE do read the posting guide! Received on Tue Jun 07 12:17:18 2005

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