# Calculating the second order derivative with and without penalty.

### Description

Calculating the second order derivative of the likelihood function of the pencopula approach w.r.t. the parameter b. Thereby, for later use, the program calculates the second order derivative with and without the penalty. Moreover, Derv2 seperates the calculation for temporary weights b in iteration and final weights b.

### Usage

1 |

### Arguments

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

`temp` |
smoothing parameter lambda |

### Details

We approximate the second order derivative in this approach with the negative fisher information.

### Value

`Derv2.pen` |
second order derivative w.r.t. beta with penalty |

`Derv2.cal` |
second order derivative w.r.t. beta without penalty. Needed for calculating of e.g. AIC. |

Derv2.cal and Derv2.pen are saved in the environment.

### Author(s)

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

### References

Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.