Dual cones, dual norms, and simultaneous inference for partially ordered means

• 成果类型: Article
• 署名作者: Berk, R; Marcus, R
• 署名单位: VOLCANI INSTITUTE OF AGRICULTURAL RESEARCH
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291410
• 发表日期: 1996
• 页码: 318-328
• 关键词: tests

摘要

Exact simultaneous one-sided confidence intervals for contrasts in m normal means are discussed. The set K of Contrast vectors considered is of one of two forms: Either it is a cone whose coordinates are monotone for a partial ordering defined on the coordinate index set (1,...,m) or it is the polar of such a cone. It is shown that the intervals obtained are inverted from test statistics that may be used for testing the null hypothesis that the mean vector mu lies in the dual (or negative polar) cone of K, against the alternative that mu is not in the dual of K. Corresponding conservative two-sided intervals are also discussed. The structure of such cones is considered and results concerning dual norms for such cones are obtained. Illustrations for simple ordering, simple-tree, and umbrella orderings are discussed.