pencopula (version 0.2.1)

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. (2011), to appear.