## Seminars

## Seminars

## On Factor Modeling of Matrix Sequences

**Holder：** Xinbing Kong (Nanjing Audit University)

**Time：**2023-11-30 15:10-17:00

**Location：**Room 217, Guanghua Building 2

**Abstract: **
In this talk, I first present some recent studies on factor modeling for matrix sequences. After that, I introduce a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers.

Later on, we consider the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Although tests are based on a randomization which does not vanish asymptotically, we propose a de-randomized, strong (based on the Law of the Iterated Logarithm) decision rule to choose in favour or against the presence of common factors. We further cast our individual tests in a sequential procedure whose output is an estimate of the number of common factors. Our tests are built on two variants of the sample second moment matrix of the data: one based on a row (or column) flattened version of the matrix-valued sequence, and one based on a projection-based method.

**About the Speaker: **

孔新兵，现为南京审计大学教授，博士生导师。主要研究兴趣为高频与高维数据统计推断与机器学习；2011年博士毕业于香港科技大学，在统计学顶刊AoS,JASA,Biometrika, JoE, JBES发表论文20篇，独立作者3篇；主持国家自然科学基金项目3项，参与国家自然科学基金重点项目1项；现为国际统计学会选举会员，国际数理统计学会会员，中国现场统计研究会多元分析应用专业委员会副理事长，江苏省应用统计学会副理事长；获第一届统计科学技术进步奖一等奖；在全国概率统计会议等做大会报告；入选国家高层次青年人才计划。

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