{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T23:58:26Z","timestamp":1792195106141,"version":"4.4.0"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T00:00:00Z","timestamp":1674864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSERC Discovery","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"NSERC Discovery","award":["RGPIN 2018-05846"],"award-info":[{"award-number":["RGPIN 2018-05846"]}]},{"name":"Interior Universities Research Coalition","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"Interior Universities Research Coalition","award":["RGPIN 2018-05846"],"award-info":[{"award-number":["RGPIN 2018-05846"]}]},{"name":"BC Ministry of Health","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"BC Ministry of Health","award":["RGPIN 2018-05846"],"award-info":[{"award-number":["RGPIN 2018-05846"]}]},{"name":"University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with UBC-O Irving K. Barber Faculty of Science","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with UBC-O Irving K. Barber Faculty of Science","award":["RGPIN 2018-05846"],"award-info":[{"award-number":["RGPIN 2018-05846"]}]},{"name":"NSERC Discovery","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"NSERC Discovery","award":["RGPIN 2018-05846"],"award-info":[{"award-number":["RGPIN 2018-05846"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u03c72(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.<\/jats:p>","DOI":"10.3390\/e25020238","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T03:56:27Z","timestamp":1675050987000},"page":"238","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Two-Sample Tests Based on Data Depth"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7981-0708","authenticated-orcid":false,"given":"Xiaoping","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Computer Science, Mathematics, Physics and Statistics, University of British Columbia, Kelowna, BC V1V 1V7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Mathematics, Physics and Statistics, University of British Columbia, Kelowna, BC V1V 1V7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8606-570X","authenticated-orcid":false,"given":"Yuejiao","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/S0047-259X(03)00079-4","article-title":"On a new multivariate two-sample test","volume":"88","author":"Baringhaus","year":"2004","journal-title":"J. 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