SEMIPARAMETRIC INFERENCE BASED ON ADAPTIVELY COLLECTED DATA

• 成果类型: Article
• 署名作者: Lin, Licong; Khamaru, Koulik; Wainwright, Martin J.
• 署名单位: University of California System; University of California Berkeley; Rutgers University System; Rutgers University New Brunswick; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2025
• 页码: 989-1014
• 关键词: confidence-intervals; efficient estimation; regression-models

摘要

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semiparametric context: estimating the parameter vector of a generalized linear regression model contaminated by a nonparametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection and provide conditions under which the associated estimates are asymptotically normal. Our results characterize the degree of explorability required for asymptotic normality to hold. For the simpler problem of estimating a linear functional, we provide similar guarantees under much weaker assumptions. We illustrate our general theory with concrete consequences for various problems, including standard linear bandits and sparse generalized bandits, and compare with other methods via simulation studies.