Distribution-free prediction bands for non-parametric regression
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2014 · Volume 76 · Issue 1
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
Enable JavaScript for citation tools and additional paper interactions.