Training and Testing with Multiple Splits: A Central Limit Theorem for Split-Sample Estimators
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多次划分下的训练与检验：分样本估计量的中心极限定理
- 研究问题
- 如何通过多次样本划分提高训练和评估的数据利用率，并在观测被重复使用、划分间存在依赖时获得可靠且可复现的推断？
- 方法与思路
- 作者对多次划分估计取平均，建立处理划分间依赖的中心极限定理，并针对正态区间可能覆盖不足的情形提出额外推断方法。
- 材料陈述的贡献
- 摘要称，理论无需限制模型复杂度或收敛速度，并提供 p 值可复现性度量；应用展示重复交叉拟合可能提高检验功效。
- 阅读关注点
- 应核对中心极限定理的实际条件、划分次数与样本量关系、模型比较时覆盖不足的来源，以及依赖修正方法和功效比较。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未获核实；摘要未完整列出理论条件，且明确指出部分模型比较中的正态区间可能覆盖不足。
原文摘要
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate subsamples to estimate the model and to evaluate it. However, this approach has two drawbacks, since each task uses only part of the data, and different splits can lead to widely different estimates. Averaging across multiple splits, I develop an inference approach that uses more data for training, uses the entire sample for testing, and improves reproducibility. I address the statistical dependence from reusing observations across splits by proving a new central limit theorem for a large class of split-sample estimators under arguably mild and general conditions. Importantly, I make no restrictions on model complexity or convergence rates. I show that confidence intervals based on the normal approximation are valid for many applications, but may undercover in important cases of interest, such as comparing the performance between two models. I develop a new inference approach for such cases, explicitly accounting for the dependence across splits. Moreover, I provide a measure of reproducibility for p-values obtained from split-sample estimators. Finally, I apply my results to two important problems in development and public economics: predicting poverty and learning heterogeneous treatment effects in randomized experiments. I show that my inference approach with repeated cross-fitting achieves better power than existing alternatives, often enough to reveal statistical significance that would otherwise be missed.