Distribution-Free Prediction Sets

• 成果类型: Article
• 署名作者: Lei, Jing; Robins, James; Wasserman, Larry
• 署名单位: Carnegie Mellon University; Harvard University; Harvard University; Carnegie Mellon University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.751873
• 发表日期: 2013
• 页码: 278-287
• 关键词: minimum volume sets; plug-in estimator; nonparametric-estimation; bandwidth selection; density; rates

摘要

This article introduces a new approach to prediction by bringing together two different nonparametric ideas: distribution-free inference and nonparametric smoothing. Specifically, we consider the problem of constructing nonparametric tolerance/prediction sets. We start from the general conformal prediction approach, and we use a kernel density estimator as a measure of agreement between a sample point and the underlying distribution. The resulting prediction set is shown to be closely related to plug-in density level sets with carefully chosen cutoff values. Under standard smoothness conditions, we get an asymptotic efficiency result that is near optimal for a wide range of function classes. But the coverage is guaranteed whether or not the smoothness conditions hold and regardless of the sample size. The performance of our method is investigated through simulation studies and illustrated in a real data example.