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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.

MSC:

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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