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Incorporating Relative Error Criterion to Conformal Prediction for Positive Data

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Abstract

Positive data are very common in many scientific fields and applications; for these data, it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion. In prediction problems, conformal prediction provides a useful framework to construct flexible prediction intervals based on hypothesis testing, which has been actively studied in the past decade. In view of the advantages of the relative error criterion for regression problems with positive responses, in this paper, we combine the relative error criterion (REC) with conformal prediction to develop a novel REC-based predictive inference method to construct prediction intervals for the positive response. The proposed method satisfies the finite sample global coverage guarantee and to some extent achieves the local validity. We conduct extensive simulation studies and two real data analysis to demonstrate the competitiveness of the new proposed method.

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Acknowledgements

The authors wish to express their gratitude to the editor and two anonymous referees for their valuable comments and suggestions, which have enhanced the quality of the article.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Center for Data Science, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Yuxiang Luo, Yang Wei & Zhouping Li

  2. Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, 518055, People’s Republic of China

    Bing-Yi Jing

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  1. Yuxiang Luo
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  2. Yang Wei
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  3. Zhouping Li
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  4. Bing-Yi Jing
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Correspondence to Zhouping Li or Bing-Yi Jing.

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Luo, Y., Wei, Y., Li, Z. et al. Incorporating Relative Error Criterion to Conformal Prediction for Positive Data. Commun. Math. Stat. 12, 157–186 (2024). https://doi.org/10.1007/s40304-023-00360-8

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  • DOI: https://doi.org/10.1007/s40304-023-00360-8

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