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pencopula (version 0.2.1)

knots.start: Calculating the knots.

Description

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

Usage

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.

Value

  • knotsSelected and sorted marginal knots for the estimation.
  • knots.helpExtended set of knots. It is needed for calculating the distribution function, help points for the integration of the B-spline density basis.
  • k.orderOrder of the knots, corresponding to their order in the hierarchical B-spline density basis.
  • knots.tThe knots ordered with 'k.order' for further fucntions.
  • tilde.Psi.knots.dHierarchical B-Spline density basis for 'knots'.
  • tilde.Psi.knots.d.helpHierarchical B-Spline density basis for 'knots.help'.
  • All values are saved in the environment.

Details

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

References

Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.