Distribution‐free prediction bands for non‐parametric regression

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 c...

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Vydáno v:Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 76; číslo 1; s. 71 - 96
Hlavní autoři: Lei, Jing, Wasserman, Larry
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishers 2014
Blackwell Publishing Ltd
John Wiley & Sons Ltd
Oxford University Press
Témata:
Algorithms
Approximation
Conformal prediction
Data analysis
Distribution
Estimation
Finite sample property
Forecasts
Kernel density
Oracles
prediction
Prediction bands
Predictions
probability distribution
Samples
Statistical analysis
Statistics
Studies
ISSN:1369-7412, 1467-9868
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Shrnutí: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.
Bibliografie:http://dx.doi.org/10.1111/rssb.12021
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ArticleID:RSSB12021
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12021