Two-Sample Multivariate Test of Homogeneity

Given independent multivariate random samples X1, X2,.... , and Y1, Y2,..... , from distributions F and G, a test is desired for Ho: F = G against general alternatives. Consider the k • (n1+n2) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbor...

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Main Author: Ali S. Barakat
Format: Article
Language:English
Published: An-Najah National University 2003-03-01
Series:مجلة جامعة النجاح للأبحاث العلوم الطبيعية
Online Access:https://journals.najah.edu/media/journals/full_texts/two-sample-multivariate-test-homogeneity.pdf
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author Ali S. Barakat
author_facet Ali S. Barakat
author_sort Ali S. Barakat
collection DOAJ
description Given independent multivariate random samples X1, X2,.... , and Y1, Y2,..... , from distributions F and G, a test is desired for Ho: F = G against general alternatives. Consider the k • (n1+n2) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let Sk be the proportion of these choices in which the point and neighbor are in the same sample. SCHILLING proposed Sk as a test statistic, but did not indicate how to determine k. BARAKAT, QUADE, and SALAMA proposed a test statistic, which is equivalent to a sum of N Wilkoxon rank sums. The limiting distribution of the test has not been found yet. We suggest as a test statistic Tm = S Sh(m,j)و Where h (m,j) = I{jth nearest neighbor of the median m is a y}. The limiting distribution of Tm is normal. A simulation with multivariate normal data suggests that our test is generally more powerful than Schilling’s test using k = 1, 2 or 3.
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publisher An-Najah National University
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series مجلة جامعة النجاح للأبحاث العلوم الطبيعية
spelling doaj-art-a9b457b082eb4bbc8888463207b0a5982025-08-20T03:23:37ZengAn-Najah National Universityمجلة جامعة النجاح للأبحاث العلوم الطبيعية1727-21142311-88652003-03-01171253310.35552/anujr.a.17.1.650Two-Sample Multivariate Test of HomogeneityAli S. Barakat0NoneGiven independent multivariate random samples X1, X2,.... , and Y1, Y2,..... , from distributions F and G, a test is desired for Ho: F = G against general alternatives. Consider the k • (n1+n2) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let Sk be the proportion of these choices in which the point and neighbor are in the same sample. SCHILLING proposed Sk as a test statistic, but did not indicate how to determine k. BARAKAT, QUADE, and SALAMA proposed a test statistic, which is equivalent to a sum of N Wilkoxon rank sums. The limiting distribution of the test has not been found yet. We suggest as a test statistic Tm = S Sh(m,j)و Where h (m,j) = I{jth nearest neighbor of the median m is a y}. The limiting distribution of Tm is normal. A simulation with multivariate normal data suggests that our test is generally more powerful than Schilling’s test using k = 1, 2 or 3.https://journals.najah.edu/media/journals/full_texts/two-sample-multivariate-test-homogeneity.pdf
spellingShingle Ali S. Barakat
Two-Sample Multivariate Test of Homogeneity
مجلة جامعة النجاح للأبحاث العلوم الطبيعية
title Two-Sample Multivariate Test of Homogeneity
title_full Two-Sample Multivariate Test of Homogeneity
title_fullStr Two-Sample Multivariate Test of Homogeneity
title_full_unstemmed Two-Sample Multivariate Test of Homogeneity
title_short Two-Sample Multivariate Test of Homogeneity
title_sort two sample multivariate test of homogeneity
url https://journals.najah.edu/media/journals/full_texts/two-sample-multivariate-test-homogeneity.pdf
work_keys_str_mv AT alisbarakat twosamplemultivariatetestofhomogeneity