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Dependence Modeling

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Nonparametric estimation of simplified vine copula models: comparison of methods

Thomas Nagler
  • Corresponding author
  • Department of Mathematics, Technische Universität München, Boltzmanstraße 3, 85748 Garching, München, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Christian Schellhase
  • Centre for Statistics, Bielefeld University, Department of Business Administration and Economics, Bielefeld, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Claudia Czado
  • Department of Mathematics, Technische Universität München, Boltzmanstraße 3, 85748 Garching, München, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-06-27 | DOI: https://doi.org/10.1515/demo-2017-0007


In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.

Keywords : B-spline; Bernstein; copula; kernel; nonparametric; simulation; vine


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About the article

Received: 2016-12-27

Accepted: 2017-05-16

Published Online: 2017-06-27

Published in Print: 2017-01-26

Citation Information: Dependence Modeling, Volume 5, Issue 1, Pages 99–120, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2017-0007.

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