随机化推断与集中不等式

中文摘要 AI 辅助

随机化或基于设计的推断正成为分析随机实验数据日益流行的工具：它不需要对结果或协变量的分布作建模假设，并且假设检验和估计在有限样本中分别有效且无偏。然而，样本平均处理效应（SATE）的置信区间仍通过有限总体中心极限定理构建，其覆盖率仅为渐近的。在本工作中，我们探索一种替代方法：利用集中不等式构建具有非渐近保证的SATE置信区间。我们针对最常见的实验设计（伯努利试验和完全随机化实验）发展该方法，并提供Hoeffding型和Bernstein型置信区间。此外，我们将这些结果扩展到配对、整群和分层随机实验。我们的关键技术贡献是：针对独立同分布数据点的新型Bernstein型集中不等式，以及针对Neyman方差估计量的集中结果。

英文摘要

Randomization or design-based inference is becoming an increasingly popular tool for analysing data from randomized experiments: It does not require modelling assumptions on the distribution of outcomes or covariates, and hypothesis testing and estimation are respectively valid and unbiased in finite samples. Yet, confidence intervals for the sample average treatment effect (SATE) are still constructed via finite-population central limit theorems and their coverage is only asymptotic. In this work, we explore an alternative approach: We use concentration inequalities to construct confidence intervals for the SATE with non-asymptotic guarantees. We develop this approach for the most common experimental designs (Bernoulli trials and completely randomized experiments) and provide Hoeffding and Bernstein-type confidence intervals. Moreover, we extend these results to matched-pair, cluster and stratified randomized experiments. Our key technical contributions are a novel Bernstein-type concentration inequality for i.i.d. data points as well as a concentration result for Neyman's variance estimator.

发表机构

• École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）

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