my.bspline {pencopulaCond}

my.bspline

Description

'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.

Usage

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

Arguments

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().

Details

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

Value

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'

Author(s)

Christian Schellhase <[e-mail]>

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.

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