不可忽略缺失数据模型的统计推断方法研究

在生物医学研究中存在大量的缺失数据，随机缺失数据的统计推断已有较为成熟的理论和方法了。然而，不可忽略缺失数据的统计推断虽有一些零散研究，但很不成熟、很不完善。因此，本项目的选题具有非常重要的理论意义和现实价值。本项目主要研究：（1）基于不可忽略缺失数据机制的某一特定模型探索模型的可识别性条件，并提出插补缺失数据的新方法及其算法；（2）对带有不可忽略缺失数据的发散维和高维或超高维半参数估计方程发展一套稳健的参数估计理论及其算法，基于Sieve的思想提出新的变量选择方法并建立其渐近理论，提出检验参数线性函数的检验统计量，研究估计方程的影响分析和拟合优度评价；（3）对带有不可忽略缺失数据的半参数指数族模型（包括：测量误差、随机效应）和分位数回归及Copula函数模型建立稳健参数估计理论、新的贝叶斯变量选择准则及其算法；（4）对没有似然函数的不可忽略缺失数据模型发展新的贝叶斯影响分析方法及算法。

There are a lot of missing data in biomedical studies. Existing theories and methods were developed on the basis of the assumption that missing data mechanism is ignorable. However, there is only a little work done on nonignorable missing data. Hence, it is meaningful to develop new theories and methods to deal with nonignorable missing data. The project aims to (i) study the problem of identifiability for a specified nonignorable missing data model, and propose some novel approaches to imput missing data; (ii) develop new theories and computing algorithms to estimate parameters and nonparametric functions in high-dimensional or ultra-high dimensional or semiparametric estimating equations with nonignorable missing data, propose some novel variable selection method based on Siever idea and develop the corresponding asymptotic theories, present some novel test statistics for testing linear function of parameters and goodness-of-fit for assessing the plausibility of the posited estimating equations and influence analysis methods for identifying influential observations; (iii) propose a robust approach to estimate parameters and random effects and a new Bayesian variable selection criterion and the corresponding algorithm in semiparametric exponential family model including measurement error models and random-effect models, and quantile regression models and Copula functional models with nonignorable missing data; (iv) develop new Bayesian influence analysis method and algorithm for a model with nonignorable missing data but without likelihood function.