Calculating the knots.

Description

Calculating the equidistant knots for the estimation. Moreover, transformation of the knots are possible.

Usage

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  knots.start(penden.env)
  knots.transform(d,alpha = 0, symmetric = TRUE)
  knots.order(penden.env)

Arguments

penden.env

Containing all information, environment of pencopula()

d

Hierarchy level of the marginal hierarchical B-spline basis.

alpha

Default = 0. Alpha is a tuning parameter, shifting the knots.

symmetric

Default = TRUE. If FALSE, the knots are selected without symmetry.

Details

'Knots.order' sorts the knots in the order, in which they disappear in the hierarchical B-spline basis.

Value

knots

Selected and sorted marginal knots for the estimation.

knots.help

Extended set of knots. It is needed for calculating the distribution function, help points for the integration of the B-spline density basis.

k.order

Order of the knots, corresponding to their order in the hierarchical B-spline density basis.

knots.t

The knots ordered with 'k.order' for further fucntions.

tilde.Psi.knots.d

Hierarchical B-Spline density basis for 'knots'.

tilde.Psi.knots.d.help

Hierarchical B-Spline density basis for 'knots.help'.

All values are saved in the environment.

Author(s)

Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

References

Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.