ck function

Calculating the actual weights ck

Calculating the actual weights ck for each factor combination of the covariates combinations.

ck(penden.env, beta.val)

Arguments

• penden.env: Containing all information, environment of pendensity()
• beta.val: actual parameter beta

Details

The weights in depending of the covariate 'x' are calculated as follows.

$c_k(x,\beta)=\frac{\exp(Z(x)\beta_k)}{\sum_{j=-K}^{K}\exp(Z(x)\beta_j)}$

For estimations without covariates, Z doesn't appear in calculations.

$c_k(\beta)=\frac{\exp(\beta_k)}{\sum_{k=-K}^{K}\exp(\beta_k)}$

Starting density calculation, the groupings of the covariates are indexed in the main program. The groupings are saved in 'x.factor', the index which response belongs to which group is saved in 'Z.index'. Therefore, one can link to the rows in 'x.factor' to calculate the weights 'ck'.

The needed values are saved in the environment.

Returns

Returning the actual weights ck, depending on the actual parameter beta in a matrix with rows.

References

Density Estimation with a Penalized Mixture Approach, Schellhase C. and Kauermann G. (2012), Computational Statistics 27 (4), p. 757-777.

Author(s)

Christian Schellhase cschellhase@wiwi.uni-bielefeld.de