Zhou Jing

In order to further promote the School's international cooperation and exchange, and better serve the university's international development and talent strengthening needs, the School of Mathematics, Physics and Statistics invited Prof. Jiyuan Tao from Loyola University Maryland to attend the 2024 International Conference on Optimization and Statistics with Applications from June 21st to June 23rd. Prof. Tao gave an academic report entitled "On the independence of linear and quadratic forms in matrix normal distribution and Wishart distribution".

Prof. Tao began by replacing random normalvectors with random normal matrices and Wishart variables, showing the interrelation between the independence of linear forms, quadratic forms andtrace forms in matrix normal and Wishart distributions. Secondly, it is proved that the Craig-Sakamoto theorem can still establish the independence of two quadratic forms in the matrix normal distribution, but it cannot establish the independence of two quadratic forms in the Wishart variable.

At the end of the report, Prof. Tao discussed with the experts and students present and answered their questions about the Craig-Sakamoto theorem and its application in statistics. The participating experts and students deepened their understanding of the cutting-edge hot issues in this field.