Containing all information, environment of pencopula()
cal
if TRUE, the final weights of one iteration are used for
the calculation of the penalized log likelihood.
temp
if TRUE, the iteration for optimal weights is still in
progress and the temporary weights are used for calculation.
Value
pen.log.likePenalized log likelihood of the copula density.
log.likeLog-Likelihood of the copula density.
The values are saved in the environment.
Details
The calculation depends on the estimated weights b, the penalized
hierarchical B-splines Phi and the penalty paramters lambda.
$$l(b,\lambda)=\sum_{i=1}^{n} \left[ \log {\sum_{i=1}^n
\boldsymbol\Phi(u_i)} b\right]- \frac 12 b^T \boldsymbol{P}(\lambda) b$$
with
$$\boldsymbol{P}(\lambda)=\sum_{j=1}{p}\lambda_j\boldsymbol{P}_j$$
The needed values are saved in the environment.
References
Flexible Copula Density Estimation with Penalized
Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.