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dc.contributor.authorGijbels, Irène
dc.contributor.authorVeraverbeke, Noël
dc.contributor.authorOmelka, Marek
dc.date.accessioned2016-09-02T06:48:22Z
dc.date.available2016-09-02T06:48:22Z
dc.date.issued2015
dc.identifier.citationGijbels, I. et al. 2015. Partial and average copulas and association measures. Electronic journal of statistics, 9(2):2420-2474. [http://dx.doi.org/10.1214/15-EJS1077]en_US
dc.identifier.issn1935-7524 (Online)
dc.identifier.urihttp://hdl.handle.net/10394/18507
dc.identifier.urihttp://dx.doi.org/10.1214/15-EJS1077
dc.identifier.urihttp://projecteuclid.org/euclid.ejs/1447943703
dc.description.abstractFor a pair (Y1,Y2) of random variables there exist several measures of association that characterize the dependence between Y1 and Y2 by means of one single value. Classical examples are Pearson’s correlation coefficient, Kendall’s tau and Spearman’s rho. For the situation where next to the pair (Y1,Y2) there is also a third variable X present, so-called partial association measures, such as a partial Pearson’s correlation coefficient and a partial Kendall’s tau, have been proposed in the 1940’s. Following criticism on e.g. partial Kendall’s tau, better alternatives to these original partial association measures appeared in the literature: the conditional association measures, e.g. conditional Kendall’s tau, and conditional Spearman’s rho. Both, unconditional and conditional association measures can be expressed in terms of copulas. Even in case the dependence structure between Y1 and Y2 is influenced by a third variable X, we still want to be able to summarize the level of dependence by one single number. In this paper we discuss two different ways to do so, leading to two relatively new concepts: the (new concept of) partial Kendall’s tau, and the average Kendall’s tau. We provide a unifying framework for the diversity of concepts: global (or unconditional) association measures, conditional association measures, and partial and average association measures. The main contribution is that we discuss estimation of the newly-defined concepts: the partial and average copulas and association measures, and establish theoretical results for the estimators. The various concepts of association measures are illustrated on a real data exampleen_US
dc.language.isoenen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.subjectAverage copulaen_US
dc.subjectconditional copulaen_US
dc.subjectempirical copula processen_US
dc.subjectnonparametric estimationen_US
dc.subjectpartial copulaen_US
dc.subjectunconditional copulaen_US
dc.subjectsmoothingen_US
dc.subjectweak convergenceen_US
dc.titlePartial and average copulas and association measuresen_US
dc.typeArticleen_US
dc.contributor.researchID22051880 - Veraverbeke, Noël Daniël


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