Exact Hessian of the negative log-likelihood function of a
TVGEV object.
d2negLogLikFun(psi, object)Value of the parameter vetor.
A TVGEV object.
The Hessian matrix of the negative log-likelihood. When
psi is taken as the estimate of the model given in
object, the matrix should be positive semidefinite.
The Hessian matrix computation relies on the exact second order
derivatives of the GEV density w.r.t the vector
\(\boldsymbol{\theta}\) of GEV parameters, see
dGEV. The derivatives w.r.t. the vector of model
parameters \(\boldsymbol{\psi}\) are computed by chain rule
using the linear inverse link.
For now, only a fairly limited use is made of the Hessian,
hence we do not strive to optimise the computation. Note that the
Hessian used in the TVGEV estimation function
(creator of TVGEV objects) and providing the covariance
matrix vcov by inversion is a numeric one for now.
From version 0.1.8, the negLogLikFun function
(closure) shipped with a TVGEV optionally comptes the
Hessian.
if (FALSE) {
example(TVGEV)
H1 <- d2negLogLikFun(res1$estimate, object = res1)
H1 - res1$hessian
H2 <- d2negLogLikFun(res2$estimate, object = res2)
H2 - res2$hessian
}