pencopula (version 0.3.5.1)

Derv1: Calculating the first derivative of the pencopula likelihood function w.r.t. parameter b

Description

Calculating the first derivative of the pencopula likelihood function w.r.t. parameter b.

Usage

Derv1(penden.env)

Arguments

penden.env

Containing all information, environment of pencopula().

Value

Derv1.pen

first order derivation of the penalized likelihood function w.r.t. parameter b.

Derv1.pen is saved in the environment.

Details

The calculation of the first derivative of the pencopula likelihood function w.r.t. b equals $$s(b,\lambda)= {\partial l(b,\lambda)}/{\partial b}= \sum_{i=1}^n \Phi(u_i)/c(u_i,b) - P(\lambda)b$$ with $$P(\lambda)$$ is the penalty matrix, saved in the environment.

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.