JSM 2005 Online Program

Abstract #304756

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	98
Type:	Contributed
Date/Time:	Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Biometrics Section
Abstract - #304756
Title:	Simultaneous Confidence Bounds for Ratios of Linear Combinations of General Linear Model Parameters
Author(s):	David Hare*+ and John Spurrier
Companies:	University of Louisiana, Monroe and University of South Carolina
Address:	, Monroe, LA, 71209-0575, United States
Keywords:	multiple comparisons ; simultaneous ; confidence regions ; ratio ; general linear model ; Jensen
Abstract:	Consider the general linear model Y = Xß + e and linearly independent vectors of known constants K1, . . . , Kk and L such that (L^T)ß ? 0. We wish to construct simultaneous confidence bounds for ?1 = (K1^T)ß/((L^T)ß) , . . . , ?k = (Kk^T)ß/((L^T)ß). Jensen (1989) has provided conservative bounds based on the Sidák inequality. We provide sharper approximations using lower bounds for \|corr(Ti(?i0), Tj(?j0))\|, where Ti(?i0) = ((K1^T)ß* - ?i(L^T)ß)/[s(mii - 2?i*mk+1,i + mk+1,k+1 (?i0)^2)]^0.5 and mij is the ijth entry in the dependence matrix. Our bound for each ?i is obtained by projecting the exact region onto the ?i-axis. If the exact region is a single contiguous bounded region, this will find the smallest rectangular solid enclosing the exact region. For k = 2, we show these minimum and maximum ?i exist either when corr(T1(?1), T2(?2)) = 0 or when ?1 and ?2 are the solution to one of the systems of equations {T1(?1) = ± c(?1, ?2), T2(?2) = ± c(?1, ?2)}. We not only improve on Jensen's bounds, but sometimes are able to reduce the number of contiguous regions and/or construct a region that is bounded while Jensen's region is unbounded.

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