quadDeriv: Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L
Description
Computes gradient and diagonal of the Hesse matrix w.r.t. to $\eta$ of a quadratic approximation to the
reparametrized original log-likelihood function
$$L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{-\infty}^{\infty} \exp(\phi(t)) dt.$$
where $L$ is parametrized via
$${\bold{\eta}}({\bold{\phi}}) = \Bigl(\phi_1, \Bigl(\eta_1+ \sum_{j=2}^i (x_i-x_{i-1})\eta_i\Bigr)_{i=2}^m\Bigr).$$
${\bold{\phi}}$: vector $(\phi(x_i))_{i=1}^m$ representing concave, piecewise linear function $\phi$,
${\bold{\eta}}$: vector representing successive slopes of $\phi.$