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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9510

Title: Improved kernel estimation of copulas: weak convergence and goodness-of-fit testing
Authors: OMELKA, Marek
Gijbels, I.
VERAVERBEKE, Noel
Issue Date: 2009
Publisher: INST MATHEMATICAL STATISTICS
Citation: ANNALS OF STATISTICS, 37(5B). p. 3023-3058
Abstract: We reconsider the existing kernel estimators for a copula function, as proposed in (1) Gijbels and Mielniczuk (1990), (2) Fermanian et al. (2004) and (3) Chen and Huang (2007). All these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many classical families of copulas. In this paper we propose improved estimators that take care of the typical corner bias problem. For (1) and (3), the improvement involves shrinking the bandwidth with an appropriate functional factor, and for (2) this is done by using a transformation. The theoretical contribution of the paper is a weak convergence result for the three improved estimators under conditions that are met for most copula families. We also discuss the choice of bandwidth parameters, theoretically and practically, and illustrate the finite-sample behaviour of the estimators in a simulation study. The improved estimators are applied to goodness-of-fit testing for copulas.
Notes: Reprint Address: Omelka, M (reprint author), Charles Univ Prague, Jaroslav Hajek Ctr Theoret & Appl Stat, Sokolovska 83, Prague 18675 8, Czech Republic - Addresses: 1. Charles Univ Prague, Jaroslav Hajek Ctr Theoret & Appl Stat, Prague 18675 8, Czech Republic 2. Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium 3. Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, B-3001 Louvain, Belgium 4. Hasselt Univ, Ctr Stat, B-3590 Diepenbeek, Belgium
URI: http://hdl.handle.net/1942/9510
DOI: 10.1214/08-AOS666
ISI #: 000268605000015
ISSN: 0090-5364
Category: A1
Type: Journal Contribution
Validation: ecoom, 2010
Appears in Collections: Research publications

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