Akio Kudô

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

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 θis 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 .

An approximate formula for Pu,K) used in order restricted inferences, and the analysis of freezing dates of lake mendota

An approximate formula for the probabilities p(l,k) which play an important role in the statistical inferences under simple order restriction, is proposed. The approximation is found to be quite satisfactory. The values of p(l,k) are presented for l=(1)k, k=2(1)15. The data on the freezing date of Lake Mendota refered in Barlow et al (1972) is analyzed by the likelihood ratio test derived in Kudo et al (1981) under the assumption of normality.