Probit Transformation for Nonparametric Kernel Estimation of the Copula Density
Arthur Charpentier () and
Davy Paindaveine ()
Working Papers ECARES from ULB -- Universite Libre de Bruxelles
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.
Keywords: copula density; transformation kernel density estimator; boundary bias; unbounded Density; local likelihood density estimation (search for similar items in EconPapers)
Pages: 41 p.
New Economics Papers: this item is included in nep-dcm and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12) Track citations by RSS feed
Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/1599 ... INDAVEINE-probit.pdf 2014-23-GEENENS_CHARPENTIER_PAINDAVEINE-probit (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2013/159977
Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/159977
Access Statistics for this paper
More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().