Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/14399
Title: Bootstrapping the conditional copula
Authors: OMELKA, Marek 
VERAVERBEKE, Noel 
Gijbels, Irene
Issue Date: 2013
Publisher: ELSEVIER SCIENCE BV
Source: JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 143 (1), p. 1-23
Abstract: This paper is concerned with inference about the dependence or association between two random variables conditionally upon the given value of a covariate. A way to describe such a conditional dependence is via a conditional copula function. Nonparametric estimators for a conditional copula then lead to nonparametric estimates of conditional association measures such as a conditional Kendall's tau. The limiting distributions of nonparametric conditional copula estimators are rather involved. In this paper we propose a bootstrap procedure for approximating these distributions and their characteristics, and establish its consistency. We apply the proposed bootstrap procedure for constructing confidence intervals for conditional association measures, such as a conditional Blomqvist beta and a conditional Kendall's tau. The performances of the proposed methods are investigated via a simulation study involving a variety of models, ranging from models in which the dependence (weak or strong) on the covariate is only through the copula and not through the marginals, to models in which this dependence appears in both the copula and the marginal distributions. As a conclusion we provide practical recommendations for constructing bootstrap-based confidence intervals for the discussed conditional association measures. (C) 2012 Elsevier B.V. All rights reserved.
Notes: [Gijbels, Irene] Katholieke Univ Leuven, Dept Math, B-3001 Heverlee, Belgium. [Gijbels, Irene] Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, B-3001 Heverlee, Belgium. [Veraverbeke, Noel] North West Univ, Unit BMI, Potchefstroom, South Africa. [Veraverbeke, Noel] Hasselt Univ, Ctr Stat, B-3590 Diepenbeek, Belgium. [Omelka, Marek] Charles Univ Prague, Fac Math & Phys, Dept Probabil & Stat, Prague 18675 8, Czech Republic. irene.gijbels@wis.kuleuven.be
Keywords: Statistics & Probability; asymptotic representation; bootstrap; empirical copula process; fixed design; random design; smoothing; weak convergence;Asymptotic representation; Bootstrap; Empirical copula process; Fixed design; Random design; Smoothing; Weak convergence
Document URI: http://hdl.handle.net/1942/14399
ISSN: 0378-3758
e-ISSN: 1873-1171
DOI: 10.1016/j.jspi.2012.06.001
ISI #: 000309845700001
Category: A1
Type: Journal Contribution
Validations: ecoom 2013
Appears in Collections:Research publications

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