An-Najah National University

Ali Barakat Blogs


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  • Wednesday, January 1, 2003
  • Two-Sample Multivariate Test of Homogeneity
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  • 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.


    An-Najah University Journal for Research - Natural Sciences (A) ISSN: 1727-2114
    Volume 17 , Issue 1 , 2003, Pages: 025-033


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Ali Said Mahmoud Barakat
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