On the limiting distributions of multivariate depth-based rank sum statistics and related tests

By Yijun Zuo, Xuming He. 2006

65 citations recorded by the source corpus.

A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260]. The present paper proves the conjecture under general regularity conditions and, therefore, validates various applications of the rank sum statistic in the literature. The paper also shows that the corresponding rank sum tests can be more powerful than Hotelling's T 2 test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b9de936133fa47180f88c9702cfc0da6dcf2c581

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Citations in the corpus

Quadratic distances on probabilities: A unified foundation (2008, unknown): “Other more recent examples can be found in Fan (1997, 1998), Fan, Zhang and Zhang (2001) and Zuo and He (2006).”
Nonparametric multivariate rank tests and their unbiasedness (2012, methodology): “We also refer to the simulation study of [43] which compared the empirical powers of the Liu–Singh rank-sum test (Q) based on the depths, the Hotelling and the Hetmansperger et al.”
Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, background): “Those ranks have been considered in Liu (1992), Liu and Singh (1993), He and Wang (1997), Zuo and He (2006), Zuo and Serfling (2000), among others; see Serfling (2002) for a general introduction on statistical depth, Hallin et al. (2010) for the related concept of quantile, Lòpez-Pintado and Romo…”
A nonparametric multivariate multisample test based on data depth (2012, background): “The asymptotic distribution of this rank sum statistic, which was conjectured in Liu and Singh (1993), is proved in Zuo and He (2006).”