pencopulaCond (version 0.2)

Derv2: Calculating the second order derivative with and without penalty.

Description

Calculating the second order derivative with and without penalty.

Usage

Derv2(penden.env, temp.lam = FALSE,temp.ck=FALSE,lam.fit=NULL)

Arguments

penden.env

Containing all information, environment of pendensity()

temp.lam

Calculating with temporal smoothing parameter lambda

temp.ck

Calculating with temporal weights ck of the spline basis functions

lam.fit

Indicating if the iterations for a new lambda are running

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.

Details

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

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.

Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.