Distribution‐free prediction bands for non‐parametric regression. (3rd July 2013)

• Record Type: Journal Article
• Authors: Lei, Jing; Wasserman, Larry
• Is Part Of: Journal of the Royal Statistical Society. Volume 76:Number 1(2014:Jan.)
• Page Start: 71
• Page End: 96
• Publication Date: 2013-07-03
• Subjects: Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12021
• Languages: English
• ISSNs: 1369-7412

Abstract

<abstract abstract-type="main" id="rssb12021-abs-0001"> <title>Summary</title> <p>We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of 'conformal prediction' with non‐parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data‐driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples.</p> </abstract>