Calculating new weights b using quadratic programing.
Usage
new.weights(penden.env)
Arguments
penden.env
Containing all information, environment of pencopula()
Value
ck.val.tempCalculated new values for the weights 'b'. The add
on 'temp' means, that there is a check in the next step if the
weights 'b' have been converted or not. 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.
'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
c(u,b)>=0, sum(b)=1 and that the marginal density is uniform. All side
conditions are saved as 'AA.help' in the environment. There exists two
different algorithms, due to the fact if one works with or without an
adaptive grid for the side condition c(u,b)>=0.
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 Copula Density Estimation with Penalized
Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.