On multivariate confidence regions and simultaneous confidence limits for ratios |
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Authors: | Gary O Zerbe Eugene Laska Morris Meisner H B Kushner |
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Institution: | 1. Department of Biometrics , University of Colorado School of Medicine , Denver, Colorado, 80262, U.S.A;2. Rockland Research Institute , Orangeburg, New York, 10962, U.S.A |
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Abstract: | Convenient general linear model computational procedures are presented for constructing multivariate confidence regions and simultaneous confidence limits for ratios of linear combinations of the parameters. The practical consequence is that a single general linear model computer program, capable of validating the underlying model and estimating the parameters, can (after slight modification) also construct the confidence regions, and even determine their precise analytic form (ellipsoid, hyperboloid, etc.). The text is deliberately factual while the appendices extend and help clarify earlier work by Henry Scheffe. As an example, a confidence ellipse and simultaneous confidence limits are constructed for several relative potencies in a classical multiple parallel line bioassay. |
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Keywords: | multivariate Fieller's theorem confidence ellipoids for ratios Scheffe simultaneous confidence intervals for relative potencies multiple bioassay |
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