题目：Manifold Principal Component Analysis and Matrix Elliptical Factor Model

报告人：孔新兵 教授 (南京审计大学)

地点：致远楼101室

时间：2024年5月20日 星期一 20:00-21：00

摘要：In this talk, we, for the first time, propose the matrix elliptical factor model, by taking the heavy tails of observations (e.g., financial returns) into consideration. Manifold principal 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 find the “center” of the locally estimated spaces across all observations, while all existing PCA methods first integrate data across observations and then do 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 are derived under mild conditions. Asymptotic distribution of the standard error for the empirical subspace “center” deviating from the population one is provided, which is of independent interest. In the end, we provide robust and consistent estimators of the row/column factor numbers based on the eigenvalue-ratio approach. Numerical studies and real example on financial returns check the flexibility of our model and the validity of the MPCA methods.

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