Statistics and Computing

, Volume 24, Issue 6, pp 1081–1100

Flexible pair-copula estimation in D-vines using bivariate penalized splines


DOI: 10.1007/s11222-013-9421-5

Cite this article as:
Kauermann, G. & Schellhase, C. Stat Comput (2014) 24: 1081. doi:10.1007/s11222-013-9421-5


The paper presents a new method for flexible fitting of D-vines. Pair-copulas are estimated semi-parametrically using penalized Bernstein polynomials or constant and linear B-splines, respectively, as spline bases in each knot of the D-vine throughout each level. A penalty induce smoothness of the fit while the high dimensional spline basis guarantees flexibility. To ensure uniform univariate margins of each pair-copula, linear constraints are placed on the spline coefficients and quadratic programming is used to fit the model. The amount of penalizations for each pair-copula is driven by a penalty parameter which is selected in a numerically efficient way. Simulations and practical examples accompany the presentation.


D-vine Copula density estimation Bernstein polynomial B-splines Penalized spline smoothing 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of StatisticsLudwig-Maximilians-University MunichMunichGermany
  2. 2.Department for Business Administration and EconomicsBielefeld UniversityBielefeldGermany

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