Abstract #302367

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JSM 2003 Abstract #302367
Activity Number: 354
Type: Topic Contributed
Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #302367
Title: Generalized p Values and Generalized Confidence Regions for the Multivariate Behrens-Fisher Problem and MANOVA
Author(s): Jinadasa K. Gamage*+ and Thomas Mathew
Companies: Illinois State University and University of Maryland, Baltimore County
Address: Mathematics Department, Normal, IL, 61790-4520,
Keywords:
Abstract:

For two multivariate normal populations with unequal covariance matrices, a procedure is developed for testing the equality of the mean vectors based on the concept of generalized p values. The generalized p value we developed is a function of the sufficient statistics. The computation of generalized p value is discussed and illustrated with an example. Numerical results show that the test based on generalized p values has a Type I error probability less than the nominal level. The problem of constructing a confidence region for the difference between the mean vectors is also addressed using the concept of generalized confidence regions. A formula is provided, involving only a finite number of chi-square random variables, for computing the generalized p value and the generalized confidence region. The formula is useful in Bayesian solution as well. Finally, using the generalized p value approach, a solution is developed for the MANOVA problem, under heteroskedasticity.

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