Test of equality of normal means in the absence of independent estimator of variance |
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Authors: | A. Kudo S. Sasabuchi J.R. Choi |
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Affiliation: | Kyushu University 33 , Fukuoka, 812, Japan |
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Abstract: | Let Xl,…,Xn be normally and independently distributed with means θl,…,θnand a cornmorl variance. Thus there are n observations and n+i unknwon parameters. A test of the null hypothesis that, the θi's are all zero and the alternative that the vector (θl,…,θn) lies in a convex cone with its vertex a.t the origin is connsidered in this paper. It is shown that under a mild condition the likelihood ratio test is possible. The ordinary one sided t - test belongs to the class of tests considered in this paper. The hypothesis of equality of means against the simple order alternative can be tested in certain cases . |
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Keywords: | order restrictions one sided t–test Likelihood ration test |
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