Victor Chernozhukov, Kaspar Wüthrich, Yinchu Zhu
arXiv 17 Sep 2019 · Econometrics · publishedProceedings of the National Academy of Sciences (2021) · 21 citations (OpenAlex)
arXiv:1909.07889 · PDF · DOI · OpenAlex · Extracted main text
We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Romano, Y., Patterson, E., and Candes, E. J (2019) Conformalized quantile regression | 1.000 | 11 | 3 | 100% |
| 2 | Lei, J., GSell, M., Rinaldo, A., Tibshirani, R. J., and Wasserman, L (2018) Distribution-free predictive inference for regression | 1.000 | 8 | 3 | 100% |
| 3 | Lei, J. and Wasserman, L (2014) Distribution-free prediction bands for non-parametric regression | 0.950 | 7 | 3 | 86% |
| 4 | Sesia, M. and Candes, E. J (2020) A comparison of some conformal quantile regression methods | 0.874 | 5 | 2 | 100% |
| 5 | Chernozhukov, V., Wüthrich, K., and Yinchu, Z (2018) Exact and robust conformal inference methods for predictive machine learning with dependent data self | 0.737 | 3 | 3 | 67% |
| 6 | Vovk, V., Gammerman, A., and Shafer, G (2005) Algorithmic Learning in a Random World | 0.737 | 3 | 2 | 100% |
| 7 | Vovk, V (2012) Conditional validity of inductive conformal predictors | 0.693 | 5 | 1 | 100% |
| 8 | Kivaranovic, D., Johnson, K. D., and Leeb, H (2020) Adaptive, distribution-free prediction intervals for deep networks | 0.644 | 2 | 2 | 100% |
| 9 | Politis, D. N (2015) Model-free prediction and regression: a transformation-based approach to inference | 0.585 | 3 | 1 | 100% |
| 10 | Chernozhukov, V., Fernandez-Val, I., and Melly, B (2013) Inference on counterfactual distributions self | 0.511 | 3 | 2 | 33% |
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