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Distribution Free Prediction Bands

Jing Lei,L. Wasserman

Published 2012 in arXiv.org

ABSTRACT

We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band estimator by combining the idea of "conformal prediction" (Vovk et al. 2009) with nonparametric conditional density estimation. The proposed estimator, called COPS (Conformal Optimized Prediction Set), always has finite sample guarantee in a stronger sense than the original conformal prediction estimator. 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 first in simulated data. Then, an application shows that the proposed method gives desirable prediction intervals in an automatic way, as compared to the classical linear regression modeling.

PUBLICATION RECORD

  • Publication year

    2012

  • Venue

    arXiv.org

  • Publication date

    2012-03-24

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1203.5422
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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REFERENCES

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