[ADMB Users] SE Estimates including process error in ADMB

dave fournier davef at otter-rsch.com
Mon Nov 15 19:00:56 PST 2010


there are inly ar efew thing to play with.  for notation let

F(x,u) be the likelihood for x and u.


    L(x) = int F(x,u) du

be what we get after integrating out u either exactly or by the laplace 

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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