面向2^K析因设计的数据自适应再随机化方法
Data-Adaptive Rerandomization for 2K Factorial Designs
- Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对2^K析因设计协变量不平衡及现有再随机化方法的局限，提出数据自适应再随机化框架，通过纳入效应优先级与协变量重要性实现精度提升，数值研究证实其效率优于现有方法。
AI中文摘要：
析因设计可同时估计多个主效应和交互效应，但协变量不平衡会大幅降低估计精度。现有再随机化方法虽能改善协变量平衡，却未充分利用析因效应间的异质性优先级或效应特异性协变量重要性。为解决这些局限，本文提出面向2^K析因设计的数据自适应再随机化框架。我们首先开发了一个先知准则，其同时纳入研究者对析因效应的优先级及效应特异性协变量重要性，可实现精度提升并带有保证下界。为使该先知准则可实施，我们开发了一种数据自适应程序，从随机单元子集学习效应特异性协变量重要性，并将估计的先知准则应用于剩余单元。与现有针对处理-对照实验的两阶段再随机化方法不同，我们的程序适配多个析因效应且无需辅助数据集。在有限总体框架下，我们建立了基于设计的渐近理论，表明所提程序保留了先知设计的精度优先属性，且在合适条件下可达到与先知设计相同的渐近精度。数值研究显示，与现有再随机化方法相比，该方法实现了显著的效率提升。
英文摘要：
Factorial designs allow simultaneous estimation of multiple main effects and interactions, but covariate imbalance can substantially reduce estimation precision. Existing rerandomization methods improve covariate balance yet do not fully exploit heterogeneous priorities across factorial effects or effect-specific covariate importance. To address these limitations, this paper proposes a data-adaptive rerandomization framework for $2^K$ factorial designs. We first develop an oracle criterion that jointly incorporates researchers' priorities over factorial effects and effect-specific covariate importance, enabling precision gains with guaranteed lower bounds. To make the oracle criterion implementable, we develop a data-adaptive procedure that learns effect-specific covariate importance from a random subset of units and applies an estimated oracle criterion to the remaining units. Unlike existing two-stage rerandomization methods for treatment-control experiments, our procedure accommodates multiple factorial effects and requires no auxiliary dataset. Under a finite-population framework, we establish design-based asymptotic theory and show that the proposed procedure preserves the oracle design's precision-prioritization property and, under suitable conditions, achieves the same asymptotic precision as the oracle design. Numerical studies demonstrate substantial efficiency gains over existing rerandomization methods.
