Calculating the penalty matrix P depends on the number of covariates 'p', the order of differences to be penalized 'pen.order', the number of observations 'n' and the penalty parameters 'lambda''.
penalty.matrix(penden.env, temp = FALSE)Containing all information, environment of pencopula().
If TRUE, the iteration for a new 'b' is not finished and a temporary penalty matrix is calculated, default = FALSE.
Penalty matrix P
The penalty matrix is calculated as
\(P(\lambda)=\sum_{j=1}^{p} \lambda_j P_j\)
with
\(P_j=\left(\bigotimes_{l=1}^{j-1}{I}\right) \otimes \{({A^{-1})^T} P {A}^{-1}\} \otimes \left(\bigotimes_{l=j+1}^p {I}\right)\)
The needed values are calculated or saved in the environment 'penden.env'.
There is no penalty used for the Bernstein polynomial basis, P=0.
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.