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http://hdl.handle.net/1942/20123
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DC Field | Value | Language |
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dc.contributor.author | VERAVERBEKE, Noel | - |
dc.contributor.author | Gijbels, Irène | - |
dc.contributor.author | OMELKA, Marek | - |
dc.date.accessioned | 2015-12-23T11:13:24Z | - |
dc.date.available | 2015-12-23T11:13:24Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Electronic journal of statistics, 9 (2), p. 2420-2474 | - |
dc.identifier.issn | 1935-7524 | - |
dc.identifier.uri | http://hdl.handle.net/1942/20123 | - |
dc.description.abstract | For 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 example. | - |
dc.description.sponsorship | This research was supported by the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy). The first author gratefully acknowledges support from the GOA/12/014 project of the Research Fund KU Leuven. The second author gratefully acknowledges support from the grant GACR 15-04774Y. The third author is an extraordinary professor at the North-West University, Potchefstroom, South Africa. The authors are grateful to an Associate Editor and two referees for their valuable comments that led to a considerable improvement of the paper. | - |
dc.language.iso | en | - |
dc.subject.other | average copula; conditional copula; empirical copula process; nonparametric estimation; partial copula; unconditional copula; smoothing; weak convergence | - |
dc.title | Partial and average copulas and association measures | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 2474 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 2420 | - |
dc.identifier.volume | 9 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Gijbels, I (reprint author), Katholieke Univ Leuven, Dept Math, Leuven, Belgium. Irene.Gijbels@wis.kuleuven.be; omelka@karlin.mff.cuni.cz; noel.veraverbeke@uhasselt.be | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1214/15-EJS1077 | - |
dc.identifier.isi | 000366270900032 | - |
item.contributor | VERAVERBEKE, Noel | - |
item.contributor | Gijbels, Irène | - |
item.contributor | OMELKA, Marek | - |
item.fullcitation | VERAVERBEKE, Noel; Gijbels, Irène & OMELKA, Marek (2015) Partial and average copulas and association measures. In: Electronic journal of statistics, 9 (2), p. 2420-2474. | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2017 | - |
crisitem.journal.issn | 1935-7524 | - |
crisitem.journal.eissn | 1935-7524 | - |
Appears in Collections: | Research publications |
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euclid.ejs.1447943703.pdf | Published version | 721.09 kB | Adobe PDF | View/Open |
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