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[2602.22083] Coarsening Bias from Variable Discretization in Causal Functionals
Summary
This paper discusses the coarsening bias introduced by discretizing continuous variables in causal functionals, proposing a bias-reduced functional to enhance accuracy in statistical estimation.
Why It Matters
Understanding coarsening bias is crucial for researchers in causal inference and statistics, as it can significantly affect the accuracy of estimates derived from discretized data. This work provides a framework to mitigate such biases, improving the reliability of causal analysis in various applications.
Key Takeaways
- Discretization of continuous variables can induce significant approximation bias in causal functionals.
- The proposed bias-reduced functional eliminates leading bias terms, enhancing estimation accuracy.
- Simulations indicate that the new method achieves near-nominal confidence interval coverage even with coarse binning.
- The findings are relevant for researchers dealing with causal inference and statistical modeling.
- The study highlights the importance of careful variable treatment in statistical analyses.
Statistics > Methodology arXiv:2602.22083 (stat) [Submitted on 25 Feb 2026] Title:Coarsening Bias from Variable Discretization in Causal Functionals Authors:Xiaxian Ou, Razieh Nabi View a PDF of the paper titled Coarsening Bias from Variable Discretization in Causal Functionals, by Xiaxian Ou and 1 other authors View PDF Abstract:A class of causal effect functionals requires integration over conditional densities of continuous variables, as in mediation effects and nonparametric identification in causal graphical models. Estimating such densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even under correct identification. Under smoothness conditions, we show that this coarsening bias is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple bias-reduced functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading term and yielding a second-order approximation error. We derive plug-in and one-step estimators for the bias-reduced functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a...
