Statistical Science

Multivariate Nonparametric Tests

Hannu Oja and Ronald H. Randles

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Abstract

Multivariate nonparametric statistical tests of hypotheses are described for the one-sample location problem, the several-sample location problem and the problem of testing independence between pairs of vectors. These methods are based on affine-invariant spatial sign and spatial rank vectors. They provide affine-invariant multivariate generalizations of the univariate sign test, signed-rank test, Wilcoxon rank sum test, Kruskal–Wallis test, and the Kendall and Spearman correlation tests. While the emphasis is on tests of hypotheses, certain references to associated affine-equivariant estimators are included. Pitman asymptotic efficiencies demonstrate the excellent performance of these methods, particularly in heavy-tailed population settings. Moreover, these methods are easy to compute for data in common dimensions.

Article information

Source
Statist. Sci., Volume 19, Number 4 (2004), 598-605.

Dates
First available in Project Euclid: 18 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.ss/1113832724

Digital Object Identifier
doi:10.1214/088342304000000558

Mathematical Reviews number (MathSciNet)
MR2185581

Zentralblatt MATH identifier
1100.62567

Keywords
Affine invariance spatial rank spatial sign Pitman efficiency robustness

Citation

Oja, Hannu; Randles, Ronald H. Multivariate Nonparametric Tests. Statist. Sci. 19 (2004), no. 4, 598--605. doi:10.1214/088342304000000558. https://projecteuclid.org/euclid.ss/1113832724


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