Weights of (χ)over-bar2 distribution for smooth or piecewise smooth cone alternatives

• 成果类型: Article
• 署名作者: Takemura, A; Kuriki, S
• 署名单位: University of Tokyo; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 2368-2387
• 关键词: sided confidence bounds; INEQUALITY; FORMULA

摘要

We study the problem of testing a simple null hypothesis about the multivariate normal mean vector against smooth or piecewise smooth cone alternatives. We show that the mixture weights of the (chi)over-bar(2) distribution of the likelihood ratio test can be characterized as mixed volumes of the cone and its dual. The weights can be calculated by integration involving the second fundamental form on the boundary of the cone. We illustrate our technique by examples involving a spherical cone and a piecewise smooth cone.