Test of equality of normal means in the absence of independent estimator of variance

A. Kudo, Shoichi Sasabuchi

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Let X1,…, Xn be normally and independently distributed with means 0n,…0n and a common variance. Thus there are n observations and n+1 unknown parameters. A test of the null hypothesis that the Qs are all zero and the alternative that the vector (0,0) lies in a convex cone with its vertex at the origin is considered 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.

Original languageEnglish
Pages (from-to)659-688
Number of pages30
JournalCommunications in Statistics - Theory and Methods
Issue number7
Publication statusPublished - Jan 1 1981


All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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