时机已到：模糊断点回归设计的一类广义估计量
计量经济学
2026-04-30 v2
摘要
标准的模糊断点回归（FRD）估计量是局部多项式估计量之差的比值。我证明，无论局部多项式阶数、核函数或带宽如何，该估计量都不具有任何有限整数矩。在小样本或当断点处的处理概率不连续很小时，该估计量是重尾的。我提出了一类广义的 FRD 估计量，它由单个调优参数索引，保留了数据的所有有限矩，并嵌套了标准 FRD 和清晰（SRD）估计量。调优参数的简单确定性值在中位数偏差、中位数绝对偏差和均方根误差方面带来了显著改进。在模拟中，置信区间通常提供可靠的小样本覆盖。使用班级规模对教育成就影响的数据展示了估计量的稳定性和性能。
引用
@article{arxiv.2511.03424,
title = {The moment is here: a generalized class of estimators for fuzzy regression discontinuity designs},
author = {Stuart Lane},
journal= {arXiv preprint arXiv:2511.03424},
year = {2026}
}
备注
61 pages. This version improves the technical rigour of the proofs of several theorems and lemmas, and refines the statements where necessary. The main conclusions remain unchanged. AR confidence intervals in the simulations were previously computed incorrectly and have been corrected in this version. These corrections do not affect the qualitative conclusions of the results