CONTROLLING CONDITIONAL COVERAGE PROBABILITY IN PREDICTION

• 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/1176348673
• 发表日期: 1992
• 页码: 1110-1119
• 关键词: intervals

摘要

Suppose the variable X to be predicted and the learning sample Y(n) that was observed are independent, with a joint distribution that depends on an unknown parameter-theta. A prediction region D(n) for X is a random set, depending on Y(n), that contains X with prescribed probability-alpha. In sufficiently regular models, D(n) can be constructed so that overall coverage probability converges to alpha at rate n(-r), where r is any positive integer. This paper shows that the conditional coverage probability of D(n), given Y(n), converges in probability to alpha at a rate which usually cannot exceed n-1/2.