pencopula (version 0.2.1)

penalty.matrix: Calculating the penalty matrix P(lambda)

Description

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''.

Usage

penalty.matrix(penden.env, temp = FALSE)

Arguments

penden.env

Containing all information, environment of pencopula().

temp

If TRUE, the iteration for a new 'b' is not finished and a temporary penalty matrix is calculated, default = FALSE.

Value

• DDD.sum
  Penalty matrix P
• Matrix is saved in the environment.

Details

The penalty matrix is calculated as

$P=\sum_{j=1}^{p} \lambda_j P(\lambda)_j$

with

$P(\lambda)_j=\left(\bigotimes_{l=1}^{j-1}{I}\right) \otimes {({A^{-1})^T} P {A}^{-1}} \otimes \left(\bigotimes_{l=j+1}^p {I}\right)$

The needed values are calculated or saved in the environment 'penden.env'.

References

Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.