Probit Transformation for Nonparametric Kernel Estimation of the Copula Density

By Gery Geenens, Arthur Charpentier, Davy Paindaveine. 2014

107 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/03bc2ee46cdabf39ef8557e5573bec16fcaf97ee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Nonparametric estimation of simplified vine copula models: comparison of methods (2017, background): “Wewill extend this approach by resorting to the more general class of local polynomial likelihood estimators; see [23] for a general account and [13] in the context of bivariate copula estimation.”