【报告摘要】 The multilevel data, where variables are nested within groups at different levels, usually shows commonality and specificity cross groups. To modeling the structure of the multilevel data, we develop the hierarchical factor model which can reveal the latent factor consistent with arbitrary hierarchical organization. First, we deal with two-level data, or simply the grouped data, which can be represented by potential global factors and local factors. We propose aggregated projection method (APM), with a novel objective function for the task by maximizing the average of correlations between the latent global factors and group factors, solved through the eigen-decomposition of the aggregated projection matrix. Further, consider the multilevel data that in tree-structured representation, we recursively apply the APM to estimate the global factors in all internal node. We establish the consistency of the global/local factor number estimation, the consistency of the estimated global/local factors and loadings, and the asymptotic distributions in two levels. Comprehensive simulations show that our method outperforms state-of-the- art methods in various scenarios. Empirical analysis on United States house prices dataset and China air quality dataset demonstrate superior accuracy in factor recovery.

 

【报告人简介】 王学钦，中国科学技术大学讲席教授，2003年毕业于宾汉姆顿大学，教育部高层次人才入选者，ISI当选会员。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、中国现场统计研究会教育统计与管理分会理事长主要研究方向为大规模复杂数据的统计学理论、方法与算法；统计机器学习；精准医疗；医疗政策；风险管理和政策评估。