my.IC: Calculating the AIC-, cAIC- and BIC-value

Description

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 24(6): 1081-1100).

Nonparametric estimation of simplified vines: comparison of methods, Nagler N., Schellhase, C. and Czado, C. (2017) Dependence Modeling.