Distribution‐free prediction bands for non‐parametric regression. (3rd July 2013) - Lei, Jing; Wasserman, Larry
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.