[R] Estimate Fisher Information by Hessian from OPTIM

[Katharine Mullen]

ChenYen wrote:
> Dear All, 
> I am trying to find MLE by using "OPTIM" function.
>
> Difficult in differentiating some parameter in my objective function, I
> would like to use the returned hessian matrix to yield an estimate of
> Fisher's Information matrix.
>
> My question: Since the hessian is calculated by numerical differentiate, is
> it a reliable estimate? Otherwise I would have to do a lot of  work to write
> a second derivative on my own.
>
>  
>
> Thank you very much in advance
>
>
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>   
When the objective function is based on a smooth function (in 
particular, a mix of exponentials) then in my experience the Fisher 
information matrix is the same as estimated via the finite difference 
approximation in numericDeriv or via analytical derivatives -- e.g., for 
the results discussed in
Katharine M. Mullen, Mikas Vengris, and Ivo H. M. van Stokkum. 
Algorithms for separable nonlinear least squares with application to 
modelling time-resolved spectra. /Journal of Global Optimization/, vol 
38, n 2, 201-213, 2007 (at http://www.nat.vu.nl/~kate/jgo2005.ps)