A multivariate control quantile test using data depth

Zhenyu Liu, Reza Modarres and Mengta Yang

Computational Statistics & Data Analysis, 2013, vol. 57, issue 1, 262-270

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.

Keywords: Statistically equivalent blocks; Data depth; Nonparametric analysis; Distribution function (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:57:y:2013:i:1:p:262-270

DOI: 10.1016/j.csda.2012.06.013

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