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penRvine (version 0.2)

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

Description

Calculating the first derivative of the paircopula likelihood function w.r.t. parameter v.

Usage

Derv1(penden.env,temp=FALSE,lambda=NULL,lam.fit=FALSE)

Arguments

penden.env
Containing all information, environment of paircopula().
temp
Default=FALSE,if TRUE temporary calculations of optimal parameters are done.
lambda
Default=NULL, i.e. the saved smoothing parameter lambda in the environment is used. Alternatively, temporary values of lambda are used for optimization of lambda.
lam.fit
Default=FALSE, indicating if the first derivative is calculated to determine the next optimal penalty parameter lambda.

Value

Derv1.pen
first order derivation of the penalized likelihood function w.r.t. parameter v.
Derv1.pen is saved in the environment.

Details

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

References

Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann, G. and Schellhase, C. (2014), Statistics and Computing 24(6): 1081-1100).

Nonparametric estimation of simplified vines: comparison of methods, Nagler N., Schellhase, C. and Czado, C. (2017) Dependence Modeling.