Distributional conformal prediction

Victor Chernozhukov, Kaspar Wüthrich and Yinchu Zhu

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: 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, under overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.

Keywords: prediction intervals; conditional validity; model-free validity; quantile regression; distribution regression (search for similar items in EconPapers)
Date: 2021-11-30
New Economics Papers: this item is included in nep-dem
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Citations: View citations in EconPapers (2)

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Working Paper: Distributional conformal prediction (2021)
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