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February 2007 Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence
Christian Genest, Jean-François Quessy, Bruno Rémillard
Ann. Statist. 35(1): 166-191 (February 2007). DOI: 10.1214/009053606000000984


Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest and Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such test statistics and to compute their relative local asymptotic efficiency. Local power curves and asymptotic relative efficiencies are compared under familiar classes of copula alternatives.


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Christian Genest. Jean-François Quessy. Bruno Rémillard. "Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence." Ann. Statist. 35 (1) 166 - 191, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62058
MathSciNet: MR2332273
Digital Object Identifier: 10.1214/009053606000000984

Primary: 62G30 , 62H15
Secondary: 60G15 , 62E20

Keywords: Archimedean copula models , Asymptotic relative efficiency , contiguous alternatives , Cramér–von Mises statistics , empirical copula process , local power curve , Möbius inversion formula , tests of multivariate independence

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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