Calculating the AIC- and BIC- value of the copula density estimation. Therefore, we add the unpenalized log likelihood of the estimation and the degree of freedom, which are
my.IC(penden.env)Containing all information, environment of pencopula()
sum of twice the negative non-penalized log likelihood and mytrace
calculated mytrace as the sum of the diagonal matrix df, which results as the product of the inverse of the penalized second order derivative of the log likelihood with the non-penalized second order derivative of the log likelihood
sum of twice the non-penalized log likelihood and log(n)
AIC is calculated as \(AIC(\lambda)= - 2*l({\bf u},\hat{\bf{b}}) + 2*df(\lambda)\)
BIC is calculated as \(BIC(\lambda)= 2*l({\bf u},\hat{\bf{b}}) + 2*df(\lambda)*log(n)\)
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.