TY - JOUR

T1 - Test of equality of normal means in the absence of independent estimator of variance

AU - Kudo, A.

AU - Sasabuchi, Shoichi

PY - 1981/1/1

Y1 - 1981/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26944441873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26944441873&partnerID=8YFLogxK

U2 - 10.1080/03610928108828064

DO - 10.1080/03610928108828064

M3 - Article

AN - SCOPUS:26944441873

SN - 0361-0926

VL - 10

SP - 659

EP - 688

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 7

ER -