Premium
Distribution‐free prediction bands for non‐parametric regression
Author(s) -
Lei Jing,
Wasserman Larry
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12021
Subject(s) - minimax , estimator , parametric statistics , oracle , mathematics , statistic , computer science , conformal map , sample (material) , bandwidth (computing) , sample size determination , density estimation , mathematical optimization , algorithm , statistics , mathematical analysis , software engineering , chromatography , computer network , chemistry
Summary 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.