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Activity Number:
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485
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Type:
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Invited
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Date/Time:
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Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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Memorial
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| Abstract - #305286 |
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Title:
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Testing Multivariate Scale Difference by Depth Rank Tests
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Author(s):
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Regina Liu*+ and Kesar Singh
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Companies:
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Rutgers University and Rutgers University
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Address:
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Department of Statistics, Piscataway, NJ, 08854-8019,
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Keywords:
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data depth ; Kruskal-Wallis test ; Wilcoxon rank sum test ; multivariate scale difference
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Abstract:
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Professor Levene contributed much to the subject of scale difference detection. We use data depth to develop new rank tests for testing scale difference in multiple multivariate samples. Consider two samples from two multivariate distributions which are identical except for a possible scale difference. The sample with the larger scale would tend to be more outlying in the combined sample. Since a data depth is a measure of outlyingness, its center-outward ranking is well-suited for forming multivariate rank tests for testing scale difference in two samples. These depth rank tests can be carried out the same way as the Wilcoxon rank sum test for univariate locations. We also generalize depth rank tests to Kruskal-Wallis--type tests for testing scale homogeneity of multiple multivariate samples. Finally, as an application, we apply our tests to compare performance stability of airlines.
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