Abstract

Modern high-dimensional statistical inference often faces the problem of missing data. In recent decades, many studies have focused on this topic and provided strategies including complete-sample analysis and imputation procedures. However, complete-sample analysis discards information of incomplete samples, while imputation procedures have accumulative errors from each single imputation. In this article, we propose a new method, Sample-wise COmbined missing effect Model with penalization (SCOM), to deal with missing data occurring in predictors. Instead of imputing the predictors, SCOM estimates the combined effect caused by all missing data for each incomplete sample. SCOM makes full use of all available data. It is robust with respect to various missing mechanisms. Theoretical studies show the oracle inequality for the proposed estimator, and the consistency of variable selection and combined missing effect selection. Simulation studies and an application to the Residential Building Data also illustrate the effectiveness of the proposed SCOM. Supplementary materials for this article are available online.

 抽象的

现代高维统计推断常常面临数据缺失的问题。近几十年来，许多研究都集中在这个主题上，并提供了包括完整样本分析和插补程序在内的策略。然而，完整样本分析会丢弃不完整样本的信息，而插补程序会因每次插补而产生累积误差。在本文中，我们提出了一种新方法，即带有惩罚的样本组合缺失效应模型（SCOM），来处理预测变量中出现的缺失数据。 SCOM 不是估算预测变量，而是估计每个不完整样本的所有缺失数据所造成的综合效应。 SCOM 充分利用所有可用数据。它对于各种缺失机制来说是稳健的。理论研究表明了所提出的估计量的预言不等式，以及变量选择和组合缺失效应选择的一致性。模拟研究和住宅建筑数据的应用也说明了所提出的 SCOM 的有效性。本文的补充材料可在线获取。