统计学系系列讲座之374期

时   间：2021年6月18日（星期五）15:00-16:00

地   点：史带楼301室

主持人：张新生  教授 复旦大学管理学院统计学系

主   题：Generalized factor model for ultra-high dimensional correlated variables with mixed types

主讲人：林华珍 教授  西南财经大学统计中心主任

简    介：林华珍教授，西南财经大学统计研究中心主任, 博士生导师，IMS-fellow，教育部**学者特聘教授，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。她的主要研究方向为非参数方法、转换模型、生存数据分析、函数型数据分析、潜变量分析、时空数据分析。研究成果发表在包括国际统计学四大顶级期刊AoS、JASA、JRSSB、Biometrika和计量经济学顶级期刊JOE及JBES上。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》的Associate Editor，《数学学报》（英文）、《系统科学与数学》国内权威等编委会编委。

摘    要：

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）

统计学系 

2021-6-16