报告题目：Projected Estimation for Large-dimensional Matrix Factor Models

报 告 人：孔新兵教授 南京审计大学

报告时间：2020年7月3日 9:30-10:30

报告地点：腾讯会议 ID：709 754 043

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https://meeting.tencent.com/s/xCsc8zEhCV3V

校内联系人：朱复康 fzhu@jlu.edu.cn

报告摘要：

Large-dimensional factor models are drawing growing attention and widely applied to analyze the correlations of large datasets. Most related works focus on vector-valued data while nowadays matrix-valued or high-order tensor datasets are ubiquitous due to the accessibility to multiple data sources. In this article, we propose a projected estimation method for the matrix factor model under flexible conditions. We show that the averaged squared Frobenious norm of our projected estimators of the row (or column) loading matrix have convergence rates $\max\{(Tp_2)^{-1}, (Tp_1)^{-2}, (p_1p_2)^{-2}\}$ (or $\max\{(Tp_1)^{-1}, (Tp_2)^{-2}, (p_1p_2)^{-2}\}$), where $p_1$ and $p_2$ are the row and column dimension of each data matrix and $T$ is the number of observations. This rate is faster than the typical rates $T^{-1}$ and $\max\{(Tp_2)^{-1}, p_1^{-2}\}$ (or $\max\{(Tp_1)^{-1}, p_2^{-2}\}$) that are conceivable from the literature on vector factor models as long as the dimensions of observed data matrices are sufficiently large. An easily satisfied sufficient condition on the projection direction to achieve the given rates for the projected estimators is provided. Moreover, we established the asymptotic distributions of the estimated row and column factor loadings. We also introduced an iterative approach to consistently determine the numbers of row and column factors. Two real data examples related to financial engineering and image recognition show that the projection estimators contribute to explaining portfolio variances and achieving accurate classification of handwritten digit numbers.

报告人简介：

孔新兵，南京审计大学教授，主要研究兴趣为髙维数据分析、高频数据分析。在统计学和计量经济学顶级期刊Annals of Statistics、Journal of the American Statistical Association、Biometrika、Journal of Econometrics上发表论文10多篇。主持国家自然科学基金3项目。获香港数学会最佳博士论文奖，复旦大学管理学院优秀青年教师新星奖，江苏省应用统计最佳论文奖。入选江苏省双创计划，江苏省青蓝工程中青年学术带头人。现在任SCI杂志《Random Matrices: Theory and Applications》的副主编。