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Distribution‐free prediction bands for non‐parametric regression

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Abstract:

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.

Keywords: Conformal prediction; Finite sample property; Kernel density; Prediction bands

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/rssb.12021

Publication date: January 1, 2014

bpl/rssb/2014/00000076/00000001/art00005
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