Derv1: Calculating the first derivative of the paircopula likelihood function w.r.t. parameter b
Description
Calculating the first derivative of the paircopula likelihood function
w.r.t. parameter v.
Usage
Derv1(penden.env,temp=FALSE,lambda=NULL)
Arguments
penden.env
Containing all information, environment of
paircopula().
temp
Default=FALSE,if TRUE temporary calculations of
optimal parameters are done.
lambda
Default=NULL, i.e. the saved smoothing parameter lambda in the
environment is used. Alternatively, temporary values of lambda
are used for optimization of lambda.
Value
Derv1.penfirst order derivation of the penalized likelihood
function w.r.t. parameter v.
Derv1.pen is saved in the environment.
Details
The calculation of the first derivative of the paircopula likelihood function w.r.t. b equals
$$s(v,\lambda)= {\partial l(v,\lambda)}/{\partial v}= \sum_{i=1}^n
\Phi(u_i)/c(u_i,v) - P(\lambda)v$$
with $$P(\lambda)$$
is the penalty matrix, saved in the environment.
References
Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann G. and Schellhase C. (2012), working paper