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

[John D. Holt]

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


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

Tel 519-824-4120Ext53297/52155