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

1 2 3 | ```
knots.start(penden.env)
knots.transform(d,alpha = 0, symmetric = TRUE)
knots.order(penden.env)
``` |

`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. |

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

`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.

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

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.

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

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