Inference on strongly identified functionals of weakly identified functions

• 成果类型: Article
• 署名作者: Bennett, Andrew; Kallus, Nathan; Mao, Xiaojie; Newey, Whitney K.; Syrgkanis, Vasilis; Uehara, Masatoshi
• 署名单位: Morgan Stanley; Cornell University; Netflix, Inc.; Tsinghua University; Tsinghua University; Massachusetts Institute of Technology (MIT); Stanford University; Chan Zuckerberg Initiative (CZI)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkaf075
• 发表日期: 2026-07
• 页码: 998-1028
• 关键词: Conditional Moment Restrictions; debiased estimation; instrumental variables; penalized minimax estimators; proximal causal inference; NONPARAMETRIC INSTRUMENTAL VARIABLES; CONDITIONAL MOMENT MODELS; restrictions; regression; EFFICIENCY; causal; robust; bounds

摘要

In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and analysis of missing-not-at-random data with shadow variables, we are interested in inference on a continuous linear functional (e.g. average causal effects) of nuisance functions (e.g. NPIV regression) defined by conditional moment restrictions. These nuisance functions are often weakly identified, meaning the moment restrictions are ill-posed and may admit multiple solutions. This paper proposes a novel condition for the functional to be strongly identified (amenable to n) rate asymptotically normal estimation) even when the nuisance function remains weakly identified. The condition implies the existence of debiasing nuisance functions. We propose penalized minimax estimators for both the primary and debiasing nuisance functions. These estimators accommodate flexible function classes and, crucially, converge to fixed limits determined by the penalization, irrespective of the nuisances' identifiability. We use these penalized estimators to construct a debiased functional estimator and prove its asymptotic normality under general high-level conditions, leading to valid confidence intervals. Our method is illustrated in partially linear proximal causal inference and instrumental variable regression problems.