### 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 language | English |
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Pages (from-to) | 659-688 |

Number of pages | 30 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 10 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jan 1 1981 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*10*(7), 659-688. https://doi.org/10.1080/03610928108828064

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

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 10, no. 7, pp. 659-688. https://doi.org/10.1080/03610928108828064

}

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 -