I'm currently using the mvtnorm package to model unobserved
heterogeneity in a structural model and using optim to estimate the
model. I have got good clues that convergence is not really a problem
but the hessian matrix estimate is very bad. To overcome this problem,
I'm constructing an OPG estimator of the information matrix and I was
wondering if there were an easy way to obtain partial derivatives of
say for instance:
P1 <-
pmvnorm(lower=c(-Inf,-Inf,-Inf,-Inf),upper=c(theta1,theta2,theta3,theta4),corr=ssigma)
with respect to the mean parameters theta1, theta2, theta3, theta4 and
the non-diagonal parameters in sigma, hence $\partial P_1 / \partial
\theta_1$, etc...
I can deal with numerical or analytical partial derivatives - a
gradient would be fine since all observations share the same partial
derivative.
Stephane
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