new.weights: Calculating new weights v.

Description

Calculating new weights v using quadratic programing.

Usage

new.weights(penden.env, lambda.temp=NULL,start=FALSE)

Arguments

penden.env

Containing all information, environment of paircopula()

lambda.temp

Default=NULL, if optimal lambda is calculated, the lambda are saved temporarily, also the resulted coefficients are saved temporarily until some convergences.

start

Default=FALSE, indicating if the first calculation of new weights is running.

Value

ck.val.temp

Calculated new values for the weights 'v'. The add on 'temp' means, that there is a check in the next step if the weights 'v' have been converted (in the case of fixed lambda). If converted, the new values 'ck.val.temp' are unnoted. If not converted, 'ck.val.temp' become the ordinary 'ck.val' for the next iteration. This check is done in my.loop. If the optimal value of lambda is calculated, the coefficients 'ck.val.temp' become the ordinary 'ck.val' for the next iteration if lambda is converted. t

'ck.val.temp' is saved in the environment.

Details

The new weights are calculated solving a quadratic program. Therefore, the derivates of first and second order are needed, 'Derv1.pen' and 'Derv2.pen'. Moreover, we have to fulfill the side conditions v>=0, sum(v)=1 and that the marginal densities are uniform. All side conditions are saved as 'AA.help' in the environment.

If the quadratic program does not find a new feasible solution, the whole program terminates. For solving the quadratic program, we use the function 'solve.QP' from the R-package 'quadprog'.

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.