Article (Scientific journals)
Archimedean copula estimation using Bayesian splines smoothing techniques
Lambert, Philippe
2007In Computational Statistics and Data Analysis, 51 (12), p. 6307-6320
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Keywords :
Archimedean copula; Bayesian p-splines; Markov chains Monte Carlo; monotonicity and convexity constraints
Abstract :
[en] Copulas enable to specify multivariate distributions with given marginals. Various parametric proposals were made in the literature for these quantities, mainly in the bivariate case. They can be systematically derived from multivariate distributions with known marginals, yielding e.g. the normal and the Student copulas. Alternatively, one can restrict his/her interest to a sub-family of copulas named Archimedean. They are characterized by a strictly decreasing convex function on (0, 1) which tends to +infinity at 0 (when strict) and which is 0 at 1. A ratio approximation of the generator and of its first derivative using B-splines is proposed and the associated parameters estimated using Markov chains Monte Carlo methods. The estimation is reasonably quick. The fitted generator is smooth and parametric. The generated chain(s) can be used to build "credible envelopes" for the above ratio function and derived quantities such as Kendall's tau, posterior predictive probabilities, etc. Parameters associated to parametric models for the marginals can be estimated jointly with the copula parameters. This is an interesting alternative to the popular two-step procedure which assumes that the regression parameters are fixed known quantities when it comes to copula parameter(s) estimation. A simulation study is performed to evaluate the approach. The practical utility of the method is illustrated by a basic analysis of the dependence structure underlying the diastolic and the systolic blood pressures in male subjects. (C) 2007 Elsevier B.V. All rights reserved.
Disciplines :
Mathematics
Author, co-author :
Lambert, Philippe  ;  Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Language :
English
Title :
Archimedean copula estimation using Bayesian splines smoothing techniques
Publication date :
15 August 2007
Journal title :
Computational Statistics and Data Analysis
ISSN :
0167-9473
eISSN :
1872-7352
Publisher :
Elsevier Science Bv, Amsterdam, Netherlands
Volume :
51
Issue :
12
Pages :
6307-6320
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 29 September 2009

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