JSM 2004 - Toronto

Abstract #301819

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Activity Number: 379
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301819
Title: Some Recent Advances in Multivariate Analysis
Author(s): Samuel S. Wu*+
Companies: University of Florida
Address: 1600 SW Archer Rd. Room C2-22, Gainesville, FL, 32610,
Keywords: Fisher's method of combining tests ; Bahadur efficiency ; average power ; multivariate linear hypotheses ; multivariate location problem
Abstract:

We discuss some new findings on combining univariate tests for multivariate problems. It is well known that in a general multiparameter setting, there may not exist any unique best test. More importantly, unlike the univariate case, the power of different test procedures could vary remarkably in multivariate analysis. A Monte Carlo study indicate that the small-sample power of the combination methods is much better than the Hotelling-type tests in many cases. Relationship is established between Fisher's method of combining tests and a new class of tests that have best average power for multivariate linear hypotheses. And asymptotic efficiencies of three combination methods, when both n and p may go to infinity, help to explain when and why they perform better than Hotelling's tests. Applications in microarray analysis, QTL detection, and composite analysis of five aphasia trials are also considered.

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