Hi Doug: I was just looking at this coincidentally. When X is a vector, the
Fisher Information I_{theta} = the negative expectation of the second
derivatives of the log likelihood. So it's a matrix.  In other words,
I_theta = E(partial^2 /partial theta^2(log(X,theta).) where X is a vector.

But, even though the the Fisher Information has a seemingly nice formula, (
and this is where my confusion arose when I was dealing with this and why
I'm looking at it right
now. I have  short document that I wrote to myself  explaining it so if
anyone wants it, email me individually. It's nothing earth shattering !!!!!
) in many cases taking the that expectation is not easy so the  Fischer
Information is approximated by its empirical counterpart which is obtained
by summing each of the elements in the matrix given the n observations and
then dividing each of the elements in the matrix by n.













On Tue, Jan 22, 2013 at 3:27 PM, Douglas Bates <bates@stat.wisc.edu> wrote:

> Your question is better addressed to the R-help@R-project.org mailing
> list,
> which I am copying on this reply.
>
> You are confusing a statistical concept, the Fisher Information matrix,
> with a numerical concept, the Hessian matrix of a scalar function of a
> vector argument.
>
> The Fisher information matrix is the Hessian matrix of a particular
> function at its optimum and I have forgotten whether that function is the
> log-likelihood or negative twice the log-likelihood or ...  Rather than get
> it wrong I am sending a copy of this reply to the list where many of the
> readers will be able to answer you more reliably than I can.
>
>
> On Tue, Jan 22, 2013 at 1:22 PM, Marcos Coque Jr <mcoquejr@yahoo.com.br
> >wrote:
>
> > Dear Bates,
> >
> > I am using the fdHess function for R language.
> > And I have a question.
> >
> > What is the relationship with the Hessian and Fisher Information in your
> > function?
> > Because I think that Fisher Information=-Hessian, but I found the oposite
> > in your function.
> > Maybe I be something wrong...
> >
> > Thanks,
> >
> > Marcos
> >
>
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>
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