pencopula {pencopulaCond}

Calculating penalized (conditional) copula density with penalized hierarchical B-splines

Description

Calculating penalized (conditional) copula density with penalized hierarchical B-splines

Usage

pencopula(data,d=3,D=d,q=1,base="B-spline",max.iter=20,test.ind=FALSE,
         lambda=c(100,100),pen.order=2,data.frame=parent.frame(),cond=FALSE,
         fix.lambda=FALSE,id=NULL) 

Arguments

data

'data' contains the data. 'data' has to be a matrix or a data.frame. The number of columns of 'data' is p.

d

refers to the hierachy level of the marginal hierarchical B-spline, default is d=3.

D

referes to the maximum hierachy level, default is D=3. If D<d, it follows D<-d.

q

degree of the marginal hierarchical B-spline.

base

By default, the used marginal basis is a 'B-spline'. Second possible option is 'Bernstein', using a Bernstein polynomial basis.

max.iter

maximum number of iteration, the default is max.iter=20.

test.ind

Default=FALSE. If test.ind=TRUE, the fitted log-likelihood of each pair-copula is evaluated. If ("log.like"/"n"<0.001), where "n" is the sample size, the program set the corresponding pair copula as independence copula. We do not use this in our simulations or applications in the article.

lambda

p-dimensional vector of penalty parameters, the values can be different. Default is lambda=c(100,100).

pen.order

The order of differences for the penalization, default is pen.order=2.

data.frame

reference to the data. Default reference is the parent.frame().

cond

Determining if a conditional copula is estimated. Default=FALSE, only suitable for p=3.

fix.lambda

Default=FALSE, using the algorithm in the paper for estimating the optimal penalty parameter. If fix.lambda=TRUE, lambda is constant throughout the estimation.

id

Optional, one set id to any value. Especially important for simulations, starting with several starting values for lambda.

Value

Returning an object of class pencopula. The class pencopula consists of the environment 'penden.env', which includes all calculated values of the estimation approach. For a fast overview of the main results, one can use the function 'print.pencopula()'.

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.