Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution

• 成果类型: Article
• 署名作者: Li, Wei; Miao, Wang; Tchetgen, Eric Tchetgen
• 署名单位: Renmin University of China; Renmin University of China; Peking University; University of Pennsylvania
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad047
• 发表日期: 2023
• 页码: 913-935
• 关键词: regression-models; semiparametric regression; repeated outcomes; Missing Data

摘要

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for vn-estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.