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November 9 Math Colloquium

Rafael Hellebuyck, Augusta University

Two-sample Tests for High Dimensional Means with Prepivoting and Data Transformation

Under the direction of Santu Ghosh, PhD.

Within the medicalfield, the demand to store and analyze small sample, large variable data has become ever-abundant. Several two-sample tests for equality of means, including the revered Hotelling's T2 test, have already been established when the combined sample size of both populations exceeds the dimension of the variables. However, these tests either become unusable or output small power when the number of variables is greater than the combined sample size. We propose a test using both prepivoting and Edgeworth expansion that maintains high power in this higher dimensional scenario, known as the "large p small n" problem. Our test'snite sample performance is compared with other recently proposed tests designed to also handle the "large p small n" situation. We apply our test to a microarray gene expression data set and report competitive rates for both power and Type-I error. 

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