The power of the circular cone test: A noncentral chi‐bar‐squared distribution
作者:
Mark Conaway,
Carolyn Pillers,
Tim Robertson,
James Sconing,
期刊:
Canadian Journal of Statistics
(WILEY Available online 1990)
卷期:
Volume 18,
issue 1
页码: 63-70
ISSN:0319-5724
年代: 1990
DOI:10.2307/3315418
出版商: Wiley‐Blackwell
关键词: Chi‐bar‐squared distributions;circular cones;order‐restricted inference
数据来源: WILEY
摘要:
AbstractPincus (1975) derived the null distribution of the likelihood‐ratio test statistic for testing that the mean vector of a multivariate normal distribution is zero against the alternative that the mean vector lies in a circular cone. Under the null hypothesis, the likelihood‐ratio test statistic has a chi‐bar‐squared distribution. We extend the results of Pincus by deriving the distribution of the likelihood‐ratio test statistic under the alternative hypothesis. In a special case, the distribution is a “noncentral chi‐bar‐squared” distribution. To our knowledge, this is the first order‐restricted testing problem for which the relationship between the null and alternative distributions of the test statistic is similar to the relationship in the linear‐model setting. That is, the distribution of the likelihood‐ratio test has a central form of a distribution under the null hypothesis and a noncentral form of the same distributio
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