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High-Dimensional Behavior of Some Multivariate Two-Sample Tests


High-Dimensional Behavior of Some Multivariate Two-Sample Tests

Shi, Shan (2015) High-Dimensional Behavior of Some Multivariate Two-Sample Tests. Masters thesis, Concordia University.

Text (application/pdf)
Shi_MSc_S2016.pdf - Accepted Version


It is a difficult problem to test the equality of distribution of two independent p-dimensional (p>1) samples (of sizes m and n, say) in a nonparametric framework. It is not only because we need deal with issues such as tractability of the null distribution of test-statistics but also the fact that the latter are rarely distribution-free. Several notable nonparametric tests for comparing multivariate distributions are the multivariate runs test of Friedman and Rafsky (1979), the nearest-neighbour test of Henze (1988) and the inter-point distance-based test of Baringhaus and Franz (BF) (2004). Biswas and Ghosh (BG) (2014) recently have shown that in a high dimension, low sample-size (HDLSS) scenario, i.e. where p goes to infinity but m, n are small or fixed, all the tests mentioned do not perform well. However, the BG-test is shown to be consistent in the case of HDLSS. In this work, we study the asymptotic behaviours of BF and BG tests when m, n and p go to infinity and min(m, n) = o(p). Our results reveal when these tests are expected to work well and when they are not. Results are illustrated by simulated data.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Shi, Shan
Institution:Concordia University
Degree Name:M.A.
Date:November 2015
Thesis Supervisor(s):Sen, Arusharka
ID Code:980808
Deposited By: SHAN SHI
Deposited On:07 Jun 2016 18:39
Last Modified:18 Jan 2018 17:52
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