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Probit Transformation for Nonparametric Kernel Estimation of the Copula Density

Listed author(s):
  • Gery Geenens
  • Arthur Charpentier
  • Davy Paindaveine

Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametricallyestimating a copula density is addressed. Arguably the most popular nonparametric density estimator,the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it isheavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded densities,and kernel methods are not consistent in that case. In this paper, a kernel-type copula density estimatoris proposed. It is based on the idea of transforming the uniform marginals of the copula density intonormal distributions via the probit function, estimating the density in the transformed domain, whichcan be accomplished without boundary problems, and obtaining an estimate of the copula densitythrough back-transformation. Although natural, a raw application of this procedure was, however, seennot to perform very well in the earlier literature. Here, it is shown that, if combined with local likelihooddensity estimation methods, the idea yields very good and easy to implement estimators, fixing boundaryissues in a natural way and able to cope with unbounded copula densities. The asymptotic properties ofthe suggested estimators are derived, and a practical way of selecting the crucially important smoothingparameters is devised. Finally, extensive simulation studies and a real data analysis evidence theirexcellent performance compared to their main competitors.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2014-23.

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Length: 41 p.
Date of creation: Apr 2014
Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/159977
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