Inference based on the affine invariant multivariate Mann–Whitney–Wilcoxon statistic. (English) Zbl 1054.62071
Summary: A new affine invariant multivariate analogue of the two-sample Mann-Whitney-Wilcoxon test based on the Oja criterion function is introduced. The associated affine equivariant estimate of shift, the multivariate Hodges-Lehmann estimate, is also considered. Asymptotic theory is developed to provide approximations for the null distribution as well as for a sequence of contiguous alternatives to consider limiting efficiencies of the test and estimate. The theory is illustrated by an example.
T. P. Hettmansperger et al. [Stat. Sin. 8, 785–800 (1998; Zbl 0905.62062)] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surprisingly more efficient in the multivariate normal case. For elliptical distributions, the limiting efficiencies coincide with those of the affine invariant spatial rank methods.
T. P. Hettmansperger et al. [Stat. Sin. 8, 785–800 (1998; Zbl 0905.62062)] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surprisingly more efficient in the multivariate normal case. For elliptical distributions, the limiting efficiencies coincide with those of the affine invariant spatial rank methods.
MSC:
| 62H15 | Hypothesis testing in multivariate analysis |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G10 | Nonparametric hypothesis testing |
Citations:
Zbl 0905.62062References:
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