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A multivariate control quantile test using data depth

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  • Liu, Zhenyu
  • Modarres, Reza
  • Yang, Mengta

Abstract

The objective of this article is to present a depth based multivariate control quantile test using statistically equivalent blocks (DSEBS). Given a random sample {x1,…,xm} of Rd-valued random vectors (d≥1) with a distribution function (DF) F, statistically equivalent blocks (SEBS), a multivariate generalization of the univariate sample spacings, can be constructed using a sequence of cutting functions hi(x) to order xi,i=1,…,m. DSEBS are data driven, center-outward layers of shells whose shapes reflect the underlying geometric features of the unknown distribution and provide a framework for selection and comparison of cutting functions. We propose a control quantile test, using DSEBS, to test the equality of two DFs in Rd. The proposed test is distribution free under the null hypothesis and well defined when d≥max(m,n). A simulation study compares the proposed statistic to depth-based Wilcoxon rank sum test. We show that the new test is powerful in detecting the differences in location, scale and shape (skewness or kurtosis) changes in two multivariate distributions.

Suggested Citation

  • Liu, Zhenyu & Modarres, Reza & Yang, Mengta, 2013. "A multivariate control quantile test using data depth," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 262-270.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:262-270
    DOI: 10.1016/j.csda.2012.06.013
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    References listed on IDEAS

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    1. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    2. Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4957-4968, June.
    3. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    4. Zhenyu Liu & Reza Modarres, 2011. "Lens data depth and median," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1063-1074.
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    Cited by:

    1. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.

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