The Annals of Statistics

Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence

Christian Genest, Jean-François Quessy, and Bruno Rémillard

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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.

Article information

Ann. Statist., Volume 35, Number 1 (2007), 166-191.

First available in Project Euclid: 6 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H15: Hypothesis testing 62G30: Order statistics; empirical distribution functions
Secondary: 62E20: Asymptotic distribution theory 60G15: Gaussian processes

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


Genest, Christian; Quessy, Jean-François; Rémillard, Bruno. Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence. Ann. Statist. 35 (2007), no. 1, 166--191. doi:10.1214/009053606000000984.

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