PROBABILITY-CENTERED PREDICTION REGIONS

• 成果类型: Article
• 署名作者: BERAN, R
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349405
• 发表日期: 1993
• 页码: 1967-1981
• 关键词: intervals; bootstrap

摘要

Consider the problem of constructing a prediction region D(n) for a potentially observable variable X on the basis of a learning sample of size n. Usually, the requirement that D(n) contain X with probability alpha, conditionally on the learning sample, does not uniquely determine D(n). This paper develops a general probability-centering concept for prediction regions that extends to vector-valued or function-valued X the classical notion of an equal-tailed prediction interval. The dual requirements of probability centering and specified coverage probability determine D(n) uniquely. Several examples illustrate the scope and consequences of the proposed centering concept.