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

A. Kudo, Shoichi Sasabuchi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume10
Issue number7
DOIs
Publication statusPublished - Jan 1 1981

Fingerprint

Equality
One-sided test
Estimator
t-test
Alternatives
Convex Cone
Likelihood Ratio Test
Null hypothesis
Unknown Parameters
Zero
Vertex of a graph
Observation
Class

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Test of equality of normal means in the absence of independent estimator of variance. / Kudo, A.; Sasabuchi, Shoichi.

In: Communications in Statistics - Theory and Methods, Vol. 10, No. 7, 01.01.1981, p. 659-688.

Research output: Contribution to journalArticle

@article{aa50acdbff3d4c2ebb1c50a9141855c8,
title = "Test of equality of normal means in the absence of independent estimator of variance",
abstract = "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.",
author = "A. Kudo and Shoichi Sasabuchi",
year = "1981",
month = "1",
day = "1",
doi = "10.1080/03610928108828064",
language = "English",
volume = "10",
pages = "659--688",
journal = "Communications in Statistics - Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",
number = "7",

}

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

VL - 10

SP - 659

EP - 688

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 7

ER -