my.bspline: my.bspline
In pencopulaCond: Estimating Non-Simplified Vine Copulas Using Penalized Splines

Description Usage Arguments Details Value Author(s) References

'my.bspline' Integrates the normal B-Spline basis to a B-spline density basis. The dimension of the basis depends on the input of number of knots 'k' and of the order of the B-spline basis 'q'. 'int.my.bspline' is a function for transformation of open B-spline basis at the boundary to become a B-spline basis density.

1 2	my.bspline(h, q, knots, y, K, plot.bsp, typ) int.my.bspline(help.env)

`h`	if equidistant knots are used (default in pencopula()), h is the distance between two neighbouring knots
`q`	selected order of the B-spline basis
`knots`	selected values for the knots
`y`	values of the response variable
`K`	the number of knots for the construction of the base
`plot.bsp`	Indicator variable TRUE/FALSE if the integrated B-spline basis should be plotted
`typ`	typ==1 without open B-splines at the boundary typ==2 with open B-splines at the boundary
`help.env`	Internal environment of my.bspline().

Firstly, the function constructs the B-spline basis to the given number of knots 'K' and the given locations of the knots.

`base.den`	The integrated B-Spline base of order q
`stand.num`	The coefficients for standardization of the ordinary B-Spline basis
`knots.val`	This return is a list. It consider of the used knots 'knots.val\$val', the help knots 'knots.val\$help' and the additional knots 'knots.val\$all', used for the construction of the base and the calculation of the distribution function of each B-Spline.
`K`	The transformed value of K, due to used order 'q' and the input of 'K'

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.

Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.

pencopulaCond documentation built on May 1, 2019, 7:56 p.m.