Calculating new weights v using quadratic programing.
Usage
new.weights(penden.env, lambda.temp=NULL)
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.
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 (to appear).