# paircopula: Flexible Pair-Copula Estimation in D-vines using Bivariate... In penDvine: Flexible Pair-Copula Estimation in D-Vines using Bivariate Penalized Splines

## Description

Calculating paircopula with penalized B-splines or penalized Bernstein polynomials

## Usage

 ```1 2``` ```paircopula(data,K=8,base="Bernstein",max.iter=30,lambda=100, data.frame=parent.frame(),m=2,fix.lambda=FALSE,pen=1,q=2) ```

## Arguments

 `data` 'data' contains the data. 'data' has to be a matrix or a data.frame with two columns. `K` K is the degree of the Bernstein polynomials. In the case of linear B-spline basis functions, K+1 nodes are used for the basis functions. `base` Type of basis function, default is "Bernstein". An alternative is base="B-spline". `max.iter` maximum number of iteration, the default is max.iter=30. `lambda` Starting value for lambda, default is lambda=100. `data.frame` reference to the data. Default reference is the parent.frame(). `m` Indicating the order of differences to be penalised. Default is "m=2". `fix.lambda` Determining if lambda is fixed or if the iteration for an optimal lambda is used, default 'fix.lambda=FALSE'. `pen` 'pen' indicates the used penalty. 'pen=1' for the difference penalty of m-th order. 'pen=2' is only implemented for Bernstein polynomials, it is the penalty based on the integrated squared second order derivatives of the Bernstein polynomials. Due to numerical difficulties handling the integral of Bernstein polynomials (that is the beta function), this approach works only for K<=15. `q` Order of B-spline basis, i.e. default q=2 means linear B-spline basis.

## Details

Each paircopula is calculated using Bernstein polynomials or B-spline densities as basis functions. Optimal coefficients and optimal penalty parameter lambda are selected iteratively using quadratic programming.

## Value

Returning an object of class 'paircopula', consisting of the environment 'penden.env', which includes all values.

## Author(s)

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

## References

Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann G. and Schellhase C. (2014+), Statistics and Computing (to appear).

penDvine documentation built on May 2, 2019, 1:06 p.m.