Manifold Principle Component Analysis for Large-Dimensional Matrix Elliptical Factor Model
时间：2022-05-07
阅读量：288次
- 演讲人： 张新生（复旦大学，教授）
- 时间：2022年05月17日 周二 14:30（北京时间）
- 地点：腾讯会议750-581-912
- 主办单位：数据科学研究中心，统计学研究所
摘要：Matrix factor model has been growing popular in scientific fields such as econometrics, which serves as a two-way dimension reduction tool for matrix sequences. In this article, we for the first time propose the matrix elliptical factor model, which can better depict the possible heavy tailed property of matrix-valued data especially in finance. Manifold Principle Component Analysis (MPCA) is for the first time introduced to estimate the row/column loading spaces. MPCA first performs Singular Value Decomposition (SVD) for each “local” matrix observation and then averages the local estimated spaces across all observations, while the existing ones such as 2-dimensional PCA first integrates data across observations and then does eigenvalue decomposition of the sample covariance matrices. We propose two versions of MPCA algorithms to estimate the factor loading matrices robustly, without any moment constraints on the factors and the idiosyncratic errors. Theoretical convergence rates of the corresponding estimators of the factor loading matrices, factor score matrices and common components matrices are derived under mild conditions. We also propose robust estimators of the row/column factor numbers based on the eigenvalue-ratio idea, which are proven to be consistent. Numerical studies and real example on financial returns data check the flexibility of our model and the validity of our MPCA methods.
This is a joint work with ZeYu Li, Yong He and Xinbing Kong.
报告人简介：张新生，复旦大学管理学院教授、博士生导师，中国数学会概率统计分会常务理事。曾担任上海市数学会常务理事、中国现场统计研究会生存分析分会副理事长、教育部高等学校数学与统计学教学指导委员会统计学专业教学指导分委员会委员（2001-2005）。主要研究方向为：高维数据的统计推断、过程统计、随机过程及其应用等。在JRSSB、JMLR、JOE、中国科学等国内外权威期刊上发表学术论文60余篇。
联系人：苏中根（suzhonggen@zju.edu.cn）
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