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.
Derv2(penden.env, temp = FALSE)Containing all information, environment of pendensity()
smoothing parameter lambda
second order derivative w.r.t. beta with penalty
second order derivative w.r.t. beta without penalty. Needed for calculating of e.g. AIC.
We approximate the second order derivative in this approach with the negative fisher information.
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.