题目： A Two-Stage Optimal Subsampling Estimation for Missing Data Problems with Large-Scale Data

主讲人：王启华
讲座时间：2023年11月27日（周一）15:00-16:00
地点：综合楼615会议室
报告人简介：

王启华，中国科学院数学与系统科学研究院研究员，博士生导师，国家级高层次人才，中国科学院“百人计划”入选者。曾在北京大学、香港大学任教及在深圳大学与浙江工商大学任特聘教授，先后访问加拿大、美国、德国及澳大利亚10多所世界一流大学。主要从事复杂数据经验似然统计推断、缺失数据分析、高维数据统计分析、大规模数据分析等方面的研究，出版专著三部，在The Annals of Statistics,  JASA及Biometrika等国际重要刊物发表论文140余篇，部分工作已产生持久的学术影响。曾主持国家自然科学重点项目、多项面上项目，作为核心骨干成员先后参加了两项国家自然科学基金创新群体项目。是高维统计分会理事长，生存分析分会副理事长，中国现场统计研究会常务理事，中国概率统计学会常务理事，曾任或现任《中国科学》（中英文版）(2005-2012)、Electronic Research Archive、Ann. Inst. Stat. Math、Biostatistics & Epidemiology及《应用数学学报》英文版等刊物及《现代数学基础丛书》与《统计与数据科学丛书》的编委。

报告摘要：

A two-stage subsampling method is proposed via Poisson sampling framework. 

A small subsample of expected size $n_{1}$ is used in the first stage to estimate the parameters in the 
propensity score and the outcome regression models,  while a larger subsample of expected size $n_{2}$ is used in the computationally simple second stage to calculate  the final estimator. An attractive property of the resulting estimator is that its convergence rate is $n_{2}^{-1/2}$ rather than $n_{1}^{-1/2}$ when both the 
propensity score  and the outcome regression functions are correctly specified. 
The rate $n_{2}^{-1/2}$ is still attainable  for some important cases if only one of the two functions is correctly specified. This indicates that using a small subsample in the computationally complex first stage can reduce the computational burden with little impact on the statistical accuracy. Asymptotic normality of the resulting estimator is established and the optimal subsampling probability is derived by minimizing the asymptotic variance of the resulting estimator. 
Simulations and a real data analysis were conducted to demonstrate the empirical performance of the resulting estimator.