The variational method of moments

• 成果类型: Article
• 署名作者: Bennett, Andrew; Kallus, Nathan
• 署名单位: Cornell University; Cornell University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad025
• 发表日期: 2023
• 页码: 810-841
• 关键词: instrumental variables estimation; sample properties; models; gmm

摘要

The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by flexible function classes such as neural nets and kernel methods, while provably maintaining statistical efficiency unlike existing related minimax estimators. We also develop inference algorithms and demonstrate the empirical strengths of VMM estimation and inference in experiments.