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

[Rolf Turner]

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