2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212582We 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.Published in at http://dx.doi.org/10.1214/193940307000000130 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62H15 (Primary) 62G20 (Secondary)text