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
AIC
sum of twice the negative non-penalized log likelihood and
mytrace
cAIC
corrected AIC.
trace
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
BIC
sum 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. (2014+), Statistics and Computing (to appear).