Description Usage Arguments Details Value Author(s) References

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.

1 |

`penden.env` |
Containing all information, environment of paircopula() |

`temp` |
Default=FALSE, if TRUE temporary values of AIC, cAIC and BIC are calculated. |

AIC is calculated as
*AIC(λ)= - 2*l({\bf u},\hat{\bf{v}}) + 2*df(λ)*

cAIC is calculated as
*AIC(λ)= - 2*l({\bf u},\hat{\bf{v}}) + 2*df(λ)+(2*df*(df+1))/(n-df-1)*

BIC is calculated as
*BIC(λ)= 2*l({\bf u},\hat{\bf{v}}) + 2*df(λ)*log(n)*

`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.

Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann G. and Schellhase C. (2014+), Statistics and Computing (to appear).

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