报告简介  Abstract

Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the data volume is so large that nonuniform subsampling probabilities cannot be calculated all at once, then subsampling with replacement is infeasible to implement. This paper solves this problem using Poisson subsampling. We first derive optimal Poisson subsampling probabilities in the context of quasi-likelihood estimation under the A- and L-optimality criteria. For a practically implementable algorithm with approximated optimal subsampling probabilities, we establish the consistency and asymptotic normality of the resultant estimators. To deal with the situation that the full data are stored in different blocks or at multiple locations, we develop a distributed subsampling framework, in which statistics are computed simultaneously on smaller partitions of the full data. Asymptotic properties of the resultant aggregated estimator are investigated. We illustrate and evaluate the proposed strategies through numerical experiments on simulated and real date sets.

嘉宾简介  About the Speaker

艾明要，北京大学数学科学学院统计学教研室主任、教授、博士生导师。兼任中国数学会理事、中国概率统计学会秘书长，中国现场统计研究会常务理事，试验设计分会理事长，高维数据统计分会副理事长等。国际重要统计期刊《Statistica Sinica》、《Journal of Statistical Planning and Inference》、《Statistics and Probability Letters》、《STAT》副主编，国内核心期刊《系统科学与数学》编委，科学出版社《统计与数据科学系列丛书》编委。主要从事试验设计与分析、大数据分析和应用统计的教学和研究工作，在Ann Statist、JASA、Biometrika、《中国科学》等国内外顶尖期刊发表学术论文六十余篇，主持完成国家自然科学基金项目6项，主持国家社科基金重大招标项目子课题1项，参与完成国家科技部重点研发计划项目2项。

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