On prediction intervals based on predictive likelihood or bootstrap methods

• 成果类型: Article
• 署名作者: Hall, P; Peng, L; Tajvidi, N
• 署名单位: Australian National University; Linkoping University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/86.4.871
• 发表日期: 1999
• 页码: 871880
• 关键词: exponential-families; densities

摘要

We argue that prediction intervals based on predictive likelihood do not correct for curvature with respect to the parameter value when they implicitly approximate an unknown probability density. Partly as a result of this difficulty, the order of coverage error associated with predictive intervals and predictive limits is equal to only the inverse of sample size. In this respect those methods do not improve on the simpler,'naive' or 'estimative' approach. Moreover, in cases of practical importance the latter can be preferable, in terms of both the size and sign of coverage error. We show that bootstrap calibration of both naive and predictive-likelihood approaches increases coverage accuracy of prediction intervals by an order of magnitude, and, in the case of naive intervals, preserves that method's numerical and analytical simplicity. Therefore, we argue, the bootstrap-calibrated naive approach is a particularly competitive alternative to more conventional, but more complex, techniques based on predictive likelihood.