MINIMAX RATES FOR HETEROGENEOUS CAUSAL EFFECT ESTIMATION

• 成果类型: Article
• 署名作者: Kennedy, Edward h.; Balakrishnan, Sivaraman; Robins, James m.; Wasserman, Larry
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2369
• 发表日期: 2024
• 页码: 793-816
• 关键词: variance

摘要

Estimation of heterogeneous causal effects-that is, how effects of poli-cies and treatments vary across subjects-is a fundamental task in causal in-ference. Many methods for estimating conditional average treatment effects(CATEs) have been proposed in recent years, but questions surrounding op-timality have remained largely unanswered. In particular, a minimax theoryof optimality has yet to be developed, with the minimax rate of convergenceand construction of rate-optimal estimators remaining open problems. In thispaper, we derive the minimax rate for CATE estimation, in a H & ouml;lder-smoothnonparametric model, and present a new local polynomial estimator, givinghigh-level conditions under which it is minimax optimal. Our minimax lowerbound is derived via a localized version of the method of fuzzy hypothe-ses, combining lower bound constructions for nonparametric regression andfunctional estimation. Our proposed estimator can be viewed as a local poly-nomial R-Learner, based on a localized modification of higher-order influ-ence function methods. The minimax rate we find exhibits several interestingfeatures, including a nonstandard elbow phenomenon and an unusual inter-polation between nonparametric regression and functional estimation rates.The latter quantifies how the CATE, as an estimand, can be viewed as a re-gression/functional hybrid.