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A multivariate control quantile test using data depth


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

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 262-270

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:262-270

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    Keywords: Statistically equivalent blocks; Data depth; Nonparametric analysis; Distribution function;


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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, American Statistical Association, vol. 104(486), pages 718-734.
    2. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(11), pages 4979-4988, July.
    3. Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 51(10), pages 4957-4968, June.
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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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