[ADMB Users] SE Estimates including process error in ADMB

[Chris Gast]

Thanks again, Dave.  Could you clarify what the general entry of the
gradient uhat'(xhat) looks like?  I had thought this would be dx_i/du_j, but
I think these would all be 1's or 0's (since, for instance , Shat_1 = shat +
uhat_1).  It is likely that I am misunderstanding something.


Thanks,

Chris




-----------------------------
Chris Gast
cmgast at gmail.com


On Mon, Nov 15, 2010 at 7:00 PM, dave fournier <davef at otter-rsch.com> wrote:

> OK,
>
> there are inly ar efew thing to play with.  for notation let
>
> F(x,u) be the likelihood for x and u.
>
> let
>
>   L(x) = int F(x,u) du
>
> be what we get after integrating out u either exactly or by the laplace
> approx.
>
> and let xhat uhat(xhat) be the miximizing values.
>
> We have   the Hessians L_xx(xhat), and F_uu(xhat,uhat(xhat)
>  and the gradients  uhat'(xhat)
> Then the covariance matrix for x,u is assumed to be
>
>     L_xx^{-1}                        L_xx^{-1} * uhat'(x)
>
>      uhat'(xhat)*L_xx^{-1}    F_uu^{-1} + uhat'(xhat)*L_xx^{-1}*uhat'(x)
>
> The idea is that u-uhat(xhat) is independent of xhat  i.e the only
> correlation is between
> xhat and uhat(x)
>
> Put in transposes where necessary.
>
> For any function of x,u the covariance is computed by the delta method.
>
>
>
>
>
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