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

By Christian Genest, Jean‐François Quessy, Bruno R'emillard. 2005

120 citations recorded by the source corpus.

Deheuvels [J. Multivariate Anal. 11 (1981) 102-113] and Genest and Remillard [Test 13 (2004) 335-369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramer-von Mises statistics derived from a Mobius 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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/afdfec207421c8d39bc7e2b50e7500952aeb089c

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Citations in the corpus

Strongly consistent nonparametric tests of conditional independence (2012, background): “As further literature we mention Bakirov et al. (2006), Beran et al. (2007), Dauxois and Nkiet (1998), Fukumizu et al. (2007), Gieser and Randles (1997), Gretton et al. (2005), Kankainen (1995), Genest et al. (2007), Dette and Neumeyer (2000) with references.”
Asymptotics of empirical copula processes under non-restrictive smoothness assumptions (2010, background): “(3.7) In ( ∞([0,1]d))2, we have by Lemma A.1 in Rémillard and Scaillet [24], (αn,α ′ n) (α,α′) (n → ∞), (3.8) where α′ is an independent copy of α.”
Multivariate nonparametric test of independence (2017, background): “The paper [13] studies the limiting distribution of such statistics under contiguous sequences of alternatives and analyses asymptotic relative efficiencies in some classes of copula alternatives.”
Copula-Based Measures of Multivariate Association (2010, background): “[6], Genest and Remillard [40] as well as Genest et al. [ 42 ] define related statistics for testing multivariate independence.”
Modeling Multivariate Distributions with Continuous Margins Using the copula R Package (2010, methodology): “As an alternative to the statistic I n , Genest and R´emillard (2004) (see also Genest, Quessy, and R´emillard 2007) studied several ways to combine the 2 d − d − 1 statistics M A,n into one global statistic for testing independence.”
Risk factor contributions in portfolio credit risk models (2010, background): “Genest et al. (2007) give a recent application to tests for multivariate independence.”