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penDvine (version 0.2.2)

paircopula: Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines

Description

Calculating paircopula with penalized B-splines or penalized Bernstein polynomials

Usage

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 polynomi
q
Order of B-spline basis, i.e. default q=2 means linear B-spline basis.

Value

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

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.

References

Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines, Kauermann G. and Schellhase C. (2012), working paper