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arXiv · 0805.2305

Chernoff-Savage and Hodges-Lehmann results for Wilks' test of multivariate independence

Marc Hallin·Davy Paindaveine
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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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Marc Hallin, Davy Paindaveine. 2008-05-15. Chernoff-Savage and Hodges-Lehmann results for Wilks' test of multivariate independence. https://doi.org/10.1214/193940307000000130

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