不可忽略缺失数据的若干理论研究及其应用

不可忽略缺失数据是指缺失机制与缺失数据本身有关的数据，该类数据广泛存在于临床试验、流行病学、人口普查、民意测验等各个领域，是当今统计研究的热点和难点问题。参数是否可识别是不可忽略缺失数据研究的核心问题，也是目前尚未完全解决的重要问题。本项目以工具变量作为突破口，系统地研究不可忽略缺失数据的相关方法、理论与应用，主要包括：（一）完善工具变量方法和理论研究，建立缺失模型选择和模型平均方法；（二）创建变量选择、充分降维、多重插补、偏差修正、稳健光滑、分位数回归等统计模型和方法；（三）探究带有不可忽略缺失的超高维数据、因果推断数据、函数型数据、分类数据、生存分析数据的统计推断方法和理论；（四）在不可忽略缺失数据下研究快速变点检测和控制图的应用。本项目将现代统计研究的思想和方法融合到不可忽略缺失数据领域，从深度和广度上拓展现有的统计方法和理论，开创若干新的研究方向。

Missing data exist in many research areas, such as clinical trials, epidemiology, population census and so on. In many applications, however, the missing data are nonignorable, i.e., the propensity depends not only on observed data but also on unobserved data. Identifiability and estimation of parameters with nonignorable missing data are challenging problems in statistical theory and applications. In this project, by utilizing an instrumental variable, we study some topics and related applications with nonignorable missing data. First, we investigate instrument search, propensity model selection and model averaging. Second, variable selection, sufficient dimension reduction, multiple imputation based estimating equations, bias-corrected empirical likelihood, robust and smoothed empirical likelihood, and quantile regression methods are proposed. The asymptotic properties of the proposed estimators are studied. Third, in order to analyse five types of complex data with nonignorable missing values, including ultrahigh dimensional data, causal data, functional data, categorical data and survival data, some new methodologies and asymptotic properties are developed. Finally, we establish the quickest change detection methods and control charts with regard to nonignorable missing data, and their properties are investigated.