Open Collections

UBC Faculty Research and Publications

Two-Sample Tests Based on Data Depth Shi, Xiaoping; Zhang, Yue; Fu, Yuejiao

Abstract

In this paper, we focus on the homogeneity test that evaluates whether two multivariate samples come from the same distribution. This problem arises naturally in various applications, and there are many methods available in the literature. Based on data depth, several tests have been proposed for this problem but they may not be very powerful. In light of the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for the multivariate two-sample homogeneity test. The proposed test statistics have the same χ²(1) asymptotic null distribution. The generalization of the proposed tests into the multivariate multisample situation is discussed as well. Simulations studies demonstrate the superior performance of the proposed tests. The test procedure is illustrated through two real data examples.

Item Metadata

Title
Two-Sample Tests Based on Data Depth
Creator
Shi, Xiaoping; Zhang, Yue; Fu, Yuejiao
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2023-01-28
Description
In this paper, we focus on the homogeneity test that evaluates whether two multivariate samples come from the same distribution. This problem arises naturally in various applications, and there are many methods available in the literature. Based on data depth, several tests have been proposed for this problem but they may not be very powerful. In light of the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for the multivariate two-sample homogeneity test. The proposed test statistics have the same χ²(1) asymptotic null distribution. The generalization of the proposed tests into the multivariate multisample situation is discussed as well. Simulations studies demonstrate the superior performance of the proposed tests. The test procedure is illustrated through two real data examples.
Subject
hypothesis test; non-parametric tests; asymptotic distribution; multi-sample problem; data depth
Genre
Article
Type
Text
Language
eng
Date Available
2025-06-06
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0449054
URI
http://hdl.handle.net/2429/91295
Affiliation
Science, Irving K. Barber Faculty of (Okanagan); Non UBC; Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Citation
Entropy 25 (2): 238 (2023)
Publisher DOI
10.3390/e25020238
Peer Review Status
Reviewed
Scholarly Level
Faculty; Researcher
Rights URI
https://creativecommons.org/licenses/by/4.0/
Aggregated Source Repository
DSpace

Item Media

Item Citations and Data

Rights

CC BY 4.0