Linear spectral statistics: Theory and applications

Linear spectral statistics: Theory and applications

Linear spectral statistics: Theory and applications

Instructor : Dr. Weiming Li, Dr. Qin Wen Wang

July 15, 2023

About the Short Course 

Lectures 1 and 2: In these two courses we will review several classical results on asymptotic of eigenvalues of large-dimensional sample covariance matrix. These results include the strong convergence of the empirical spectral distribution and the CLT for linear spectral statistics. Then, we apply these theories to the inferences on population covariance matrix.

Lectures 3 and 4: In these two courses, we will introduce a kind of robust location and scatter estimators, that is, the sample spatial median and sample spatial-sign covariance matrix. Then, we talk about the asymptotic theories for its eigenvalues and related applications in statistics.​

In-Person Event. Location Of Short Courses: University of Ottawa

Who is this course for?

Graduate students and young researchers.

Level Of Instruction: Intermediate

Learning Outcomes

After completing this short course, attendants should be familiar with a range of concepts and recent results in random matrix theory, including the empirical spectral distributions, limiting spectral distributions, linear spectral statistics, etc. Moreover, they should have acquired knowledge about theoretical results on the eigenvalue distributions of certain high-dimensional random matrix models, particularly, the widely studied sample covariance matrix and spatial-sign covariance matrix. Lastly, attendants should also have acquired conceptual and practical understanding of differences between classical multivariate analysis and modern high-dimensional statistics.

Course Materials

Lecture slides

Knowledge Assumed

  •  Multivariate statistical analysis,

  •  Probability theory

  •  Residue theorem and Cauchy theorem in complex analysis

Preparatory Material

Chapters 1-2-3 of J. Yao, S. Zeng and Z. Bai, 2015. Large Sample Covariance Matrices and High-Dimensional Data Analysis. Cambridge University Press.

About the instructor: Dr. Weiming Li

Dr. Weiming Li is an Associate Professor of statistics at Shanghai University of Finance and Economics, School of Statistics and Management. Dr. Li’s research areas include random matrix theory and high-dimensional statistical inference. He is now an associate editor of CSDA journal. 

Affiliations: Weiming Li, Associate Professor, School of Statistics and Management, Shanghai University of Finance and Economics, China

About the instructor:  Dr. Qinwen Wang

Dr. Qinwen Wang is an Associate professor at School of Data Science, Fudan University. Dr. Wang’s research areas include random matrix theory and high-dimensional statistics. 

Affiliations: Associate Professor, School of Data Science, Fudan University, China