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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| Format: | Article |
| Language: | English |
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An-Najah National University
2003-03-01
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| 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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| _version_ | 1849684005317771264 |
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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. |
| format | Article |
| id | doaj-art-a9b457b082eb4bbc8888463207b0a598 |
| institution | DOAJ |
| issn | 1727-2114 2311-8865 |
| language | English |
| publishDate | 2003-03-01 |
| publisher | An-Najah National University |
| record_format | Article |
| 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 |