Abstract #301959

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JSM 2003 Abstract #301959
Activity Number: 424
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #301959
Title: Simultaneous Inference for Two Ratios of Linear Combinations
Author(s): David R. Hare*+ and John D. Spurrier
Companies: University of South Carolina, Columbia and University of South Carolina
Address: 116 Mineral Waters Dr., Lexington, SC, 29073,
Keywords: multiple comparison ; hypothesis test ; confidence interval
Abstract:

Consider the general linear model, Y = Xbeta + e, where Y is an n x 1 vector of observations, X is an n x p full-rank design matrix, beta is a p x 1 vector of unknown parameters, and e is an n-variate normally distributed vector with expectation vector 0 and covariance matrix sigma^2I. Let K1, K2 and L be linearly independent p x 1 vectors of known constants such that L'beta is not equal to 0. We will construct simultaneous confidence regions for the ratios rho1 = (K1'beta)/ (L'beta) and rho2 = (K2'beta)/ (L'beta) by inverting the hypothesis test that rho1 = rho10 and rho2 = rho20 where rho10 and rho20 are predetermined constants. Jensen has provided conservative bounds for rho1 and rho2 based on the Sidak inequality. We will provide sharper approximations or exact bounds.

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