博士生讨论班2025[24]
时间：2025-11-17
阅读量：18次
- 演讲人： 陶与杭
- 时间：2025年11月18日14:00
- 地点：浙江大学紫金港校区行政楼1417报告厅
- 主办单位：浙江大学数据科学研究中心
报告文章：Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design (Christopher Harshaw, Fredrik Sävje, Daniel A. Spielman & Peng Zhang)
摘要：The design of experiments involves a compromise between covariate balance and robustness. This article provides a formalization of this tradeoff and describes an experimental design that allows experimenters to navigate it. The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect. Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates. Less robustness allows for more balance. We show that the mean squared error of the estimator is bounded in finite samples by the minimum of the loss function of an implicit ridge regression of the potential outcomes on the covariates. Asymptotically, the design perfectly balances all linear functions of a growing number of covariates with a diminishing reduction in robustness, effectively allowing experimenters to escape the compromise between balance and robustness in large samples. Finally, we describe conditions that ensure asymptotic normality and provide a conservative variance estimator, which facilitate the construction of asymptotically valid confidence intervals. Supplementary materials for this article are available online.