Chernoff-Savage and Hodges-Lehmann results for Wilks’ test of multivariate independence
Marc Hallin, Davy Paindaveine
Abstract
We extend to rank-based tests of multivariate independence the Chernoff-Savage and Hodges-Lehmann classical univariate results. More precisely, we show that the Taskinen, Kankainen and Oja (2004) normal-score rank test for multivariate independence uniformly dominates – in the Pitman sense – the classical Wilks (1935) test, which establishes the Pitman non-admissibility of the latter, and provide, for any fixed space dimensions p, q of the marginals, the lower bound for the asymptotic relative efficiency, still with respect to Wilks’ test, of the Wilcoxon version of the same.
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Primary Subjects: 62H15
Secondary Subjects: 62G20
Keywords: asymptotic relative efficiency; Chernoff-Savage results; Hodges-Lehmann results; multivariate signs and ranks; Pitman non-admissibility; rank-based inference; test for independence
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1207058273
Digital Object Identifier: doi:10.1214/193940307000000130
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