CONFIDENCE-REGIONS IN LINEAR FUNCTIONAL-RELATIONSHIPS

• 成果类型: Article
• 署名作者: ZHANG, HP
• 署名单位: University of Virginia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325357
• 发表日期: 1994
• 页码: 49-66
• 关键词: approximate distributions; regression; variables; errors

摘要

A unified approach to deriving confidence regions in linear functional relationship models is presented, based on the conditional likelihood ratio method of Knowles, Siegmund and Zhang. In the case of a single latent predictor, the confidence region for the slope produced by this approach is the familiar one of Fieller and Creasy. However, here it is shown how to derive a confidence region for the slope, when it is known that the slope is positive, that improves on merely intersecting the region for an unrestricted slope with (0, infinity). A geometric interpretation is given for Fieller-Creasy confidence region for the ratio of population means (Fieller-Creasy problem). Regions are also derived for simultaneous estimation of the slope and intercept in the model with a single latent predictor, and for the slopes in a model with two latent predictors