Position : homepage  > 2022

Manifold Principle Component Analysis for Large-Dimensional Matrix Elliptical Factor Model

Date: 2022-05-17 Visitcount : 10

Speaker: Xinsheng Zhang (Fudan University)

Date: May 17 Tues. 2:30pm

Venue: Tencent Meeting Room: 750 581 912

Abstract: 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 “1ocal” 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 mode1 and the validity of our MPCA methods. 

This is a joint work with ZeYu Li, Yong He and Xinbing Kong.