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

From: Rolf Turner <rolf_at_math.unb.ca>
Date: Tue 07 Jun 2005 - 08:48:34 EST


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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