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
Usage
my.IC(penden.env)
Arguments
penden.env
Containing all information, environment of pencopula()
Value
AICsum of twice the negative non-penalized log likelihood and mytrace
tracecalculated 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
BICsum of twice the non-penalized log likelihood and log(n)
All values are saved in the environment.
Details
AIC is calculated as
$AIC(\lambda)= - 2*l({\bf u},\hat{\bf{b}}) + 2*df(\lambda)$
BIC is calculated as
$BIC(\lambda)= 2*l({\bf u},\hat{\bf{b}}) + 2*df(\lambda)*log(n)$
References
Flexible Copula Density Estimation with Penalized
Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.