Construction of the hierarchical B-spline density basis.

1 | ```
hierarch.bs(x, d, plot.bsp, typ, penden.env, int=FALSE)
``` |

`x` |
Marginal data for construction. |

`d` |
Hierarchy level of the marginal hierarchical B-spline density. |

`plot.bsp` |
Default = FALSE. If TRUE, each B-spline basis is plotted. |

`typ` |
typ==1 without open B-splines at the boundary typ==2 with open B-splines at the boundary. |

`penden.env` |
Containing all information, environment of pencopula(). |

`int` |
Default = FALSE. If TRUE, the integral of the hierarchical B-spline density basis is calculated (used for the distribution function of the estimation). |

First, the marginal hierarchical B-spline density basis is constructed for each covariate 'B.tilde'.

After the construction of each marginal basis, the hierarchical B-spline density basis is built in the main program pencopula(), using an object 'Index.basis.D' (saved in the environment). 'Index.basis.D' notes which compenent of the marginal basis has to be selected. In the main program the object 'tilde.Psi.d.D' is constructed. D refers to the maximum hierachy level and 'd' is the hierarchy level of the marginal hierarchical B-spline.

`B.tilde` |
'B.tilde' is the hierarchical B-spline density basis, returned by 'hierarch.bs'. |

`int.B.tilde` |
If 'int=TRUE', the integral of the hierachical B-spline density basis is calculated and returned by 'hierarch.bs'. |

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.

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