On f-tests and linear hypothesis in a general linear model |
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| Authors: | YosHimasa Ukita Kazuo Noda Etsuo Miyaoka |
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| Affiliation: | 1. General Education Course , Meisei University , 337 Hodokubo, Hino-shi, Tokyo, 191, Japan;2. Dept. of Mathematics , Science University of Tokyo , 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162, Japan |
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| Abstract: | A simple method of setting linear hypotheses testable by F-tests in a general linear model when the covariance matrix has a general form and is completely unknown, is provided. With some additional conditions imposed on the covariance matrix, there exist the UMP invariant tests of certain linear hypotheses. We derive them to compare the powers with those of F-tests obtained under no restrictions on the covariance matrix. The results are illustrated in a multiple regression model with some examples. |
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| Keywords: | general linear model F-test linear hypothesis UMP invariant test multiple regression |
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