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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