Abstract

We study the identification and estimation of statistical functionals of multivariate data missing nonmonotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called “no self-censoring” or “itemwise conditionally independent nonresponse,” which roughly corresponds to the assumption that no partially observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously studied dataset of HIV-positive mothers in Botswana. Supplementary materials for this article are available online.

摘要

我们采用半参数方法研究非单调和非随机缺失的多元数据统计泛函的识别和估计。具体来说，我们假设缺失机制满足之前所谓的“无自我审查”或“逐项条件独立无响应”，这大致对应于没有部分观察到的变量直接决定其自身缺失状态的假设。我们表明，该假设与联合密度的优势比参数化相结合，能够识别感兴趣的函数，并且我们为满足该假设的非参数模型建立了半参数效率界限。我们提出了一个实用的增强逆概率加权估计器，在具有（可能是高维）始终观察到的协变量子集的设置中，我们提出的估计器具有一定的双重稳健性。我们通过模拟实验和先前研究的博茨瓦纳 HIV 阳性母亲的数据集来探索我们的估计器的性能。本文的补充材料可在线获取。