penRvine (version 0.2)

Derv2: Calculating the second order derivative of the paircopula likelihood function w.r.t. parameter b

Description

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

Usage

Derv2(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

Derv2.pen

second order derivative w.r.t. v with penalty

Derv2.cal

second order derivative w.r.t. v 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 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.