Tolerance regions and multiple-use confidence regions in multivariate calibration

• 成果类型: Article
• 署名作者: Mathew, T; Sharma, MK; Nordström, K
• 署名单位: University System of Maryland; University of Maryland Baltimore; Johnson & Johnson; Johnson & Johnson USA; University of Helsinki
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1989-2013
• 关键词: regression; intervals

摘要

Let y(i) similar to N(Bx(i), Sigma), i = 1, 2,..., N, and y similar to N(B theta, Sigma) be independent multivariate observations, where the x(i)'s are known vectors, B, theta and Sigma are unknown, B being a positive definite matrix. The calibration problem deals with statistical inference concerning theta and the problem that we have addressed is the construction of confidence regions. In this article, we have constructed a region for theta based on a criterion similar to that satisfied by a tolerance region. The situation where theta is possibly a nonlinear function, say h(xi), of fewer unknown parameters denoted by the vector xi, is also considered. The problem addressed in this context is the construction of a region for xi. The numerical computations required for the practical implementation of our region are explained in detail and illustrated using an example. Limited numerical results indicate that our regions satisfy the coverage probability requirements of multiple-use confidence regions.