[Lecture] Huazhen Lin：Generalized factor model for ultra-high dimensional correlated variables with mixed types*
Time: 8:30-9:30am, Jun. 5th, 2021, Saturday
Venue: Tencent meeting ID：612 438 046
Spreker: Huazhen Lin, Professor, Director of the Statistical Research Center, Southwestern University of Finance and Economics
Abstract:As high-dimensional data measured with mixed-type variables gradually become prevalent, it is particularly appealing to represent those mixed-type high-dimensional data using a much smaller set of so-called factors. Due to the limitation of the existing methods for factor analysis that deal with only continuous variables, in this paper, we develop a generalized factor model, a corresponding algorithm and theory for ultra-high dimensional mixed types of variables where both the sample size $n$ and variable dimension $p$ could diverge to infinity. Specifically, to solve the computational problem arising from the non-linearity and mixed types, we develop a two-step algorithm so that each update can be carried out in parallel across variables and samples by using an existing package. Theoretically, we establish the rate of convergence for the estimators of factors and loadings in the presence of nonlinear structure accompanied with mixed-type variables when both $n$ and $p$ diverge to infinity. Moreover, since the correct specification of the number of factors is crucial to both the theoretical and the empirical validity of factor models, we also develop a criterion based on a penalized loss to consistently estimate the number of factors under the framework of a generalized factor model. To demonstrate the advantages of the proposed method over the existing ones, we conducted extensive simulation studies and also applied it to the analysis of the NFBC1966 dataset and a cardiac arrhythmia dataset, resulting in more predictive and interpretable estimators for loadings and factors than the existing factor model.
*Joint work with Wei Liu, Shurong Zheng and Jin Liu
Speaker’s Bio:林华珍 教授，博士生导师，西南财经大学统计研究中心主任, 国家杰出青年科学基金获得者，国家百千万人才工程获得者，享受国务院政府特殊津贴专家，教育部新世纪优秀人才，第十一批四川省学术和技术带头人，第十批成都市有突出贡献的优秀专家。主要研究方向为转换模型、非参数方法、生存数据分析、函数型数据分析、潜变量分析、ROC方法、偏态数据分析、捕获-再捕获数据分析， 发表学术论文40余篇，包括发表在AoS、JASA、JoE、JRSSB、Biometrika及Biometrcs等国际统计学和计量经济学顶级期刊上论文若干。先后六次主持国家自然科学基金项目。林华珍教授是国际IMS-China、IBS-CHINA及ICSA-China委员，中国现场统计研究会数据科学与人工智能分会理事长，第九届全国工业统计学教学研究会副会长，中国现场统计研究会环境与资源分会、高维数据分析分会、生物医学统计学会、生存分析分会等多个分会的副理事长。先后是国际统计学期刊《Biometrics》、《Scandinavian Journal of Statistics》、《Journal of Business & Economic Statistics》、《Canadian Journal of Statistics》、《Statistics and Its Interface》、《Statistical Theory and Related Fields》Associate Editor， 国内核心学术期刊《应用概率统计》、《系统科学与数学》、《数理统计与管理》编委。
