Distribution-free prediction bands for non-parametric regression. (English) Zbl 1411.62103

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.


62G08 Nonparametric regression and quantile regression
62G07 Density estimation
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
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