Calculating the AIC-, cAIC- and BIC- value of the paircopula density estimation. Therefore, we add the unpenalized log likelihood of the estimation and the degree of freedom.
Usage
my.IC(penden.env,temp=FALSE)
Arguments
penden.env
Containing all information, environment of
paircopula()
temp
Default=FALSE, if TRUE temporary values of AIC, cAIC and
BIC are calculated.
Value
AICsum of twice the negative non-penalized log likelihood and
mytrace
cAICcorrected AIC.
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
$AIC(\lambda)= - 2*l({\bf u},\hat{\bf{v}}) + 2*df(\lambda)$
cAIC is calculated as
$AIC(\lambda)= - 2*l({\bf u},\hat{\bf{v}}) + 2*df(\lambda)+(2*df*(df+1))/(n-df-1)$
BIC is calculated as
$BIC(\lambda)= 2*l({\bf u},\hat{\bf{v}}) + 2*df(\lambda)*log(n)$
References
Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann G. and Schellhase C. (2012), working paper