Distribution-free prediction bands for non-parametric regression

Jing Lei and Larry Wasserman

Journal of the Royal Statistical Society Series B, 2014, vol. 76, issue 1, 71-96

Abstract: type="main" xml:id="rssb12021-abs-0001">

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.

Date: 2014
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