Calculating the optimal coefficients 'b' iteratively, using quadratic programing.
my.loop(penden.env)Containing all information, environment of pencopula()
The results of each iteration are written in a matrix called 'liste', saved in the environment. 'liste' contains the penalized log-likelihood, the log-likelihood, 'lambda' and the weights 'b'.
'my.loop' optimates the log-likelihhod iteratively. Therefore, the routine checks the relative chance in the weights and stops the iteration, if the relative change of all weights 'b' is less than one percent. During the calculations of new weights 'b' in the routine 'new.weights', most of the values are called '.temp'. This add on unterlines the temporarily values. 'my.loop' checks the relative change in the weights. If the change is greater than one percent, the the real values are overwritten with the '.temp' values.
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.