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

Marc Hallin and 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.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 184-196

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058273

Digital Object Identifier
doi:10.1214/193940307000000130

Mathematical Reviews number (MathSciNet)
MR2462206

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Keywords
asymptotic relative efficiency Chernoff-Savage results Hodges-Lehmann results multivariate signs and ranks Pitman non-admissibility rank-based inference test for independence

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Hallin, Marc; Paindaveine, Davy. Chernoff-Savage and Hodges-Lehmann results for Wilks’ test of multivariate independence. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 184--196, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000130. https://projecteuclid.org/euclid.imsc/1207058273


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References

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