报告题目：Variance Variation Criterion and Consistency in Estimating the Number of Significant Signals of High-dimensional PCA

报告人：崔恒建（首都师范大学，教授）

报告时间：2022年6月3日14：00-15：30

报告地点：腾讯会议ID：521-646-433

校内联系人：李天然

报告摘要：In this talk, we will propose a criterion  based on the variance variation of  the sample eigenvalues to correctly estimate the number of significant components in high-dimensional principal component analysis, and it corresponds to the number of significant eigenvalues of the covariance matrix for p-dimensional variables. Under the rate of eigenvalues or the certainly gap condition, we can derive that the consistent properties of the proposed criterion for the situation when the significant eigenvalues tend to infinity, and when the bounded significant population eigenvalues. Numerical simulation shows that our variance variation criterion is faster than AIC and BIC converges to 1 in probability estimation under the finite fourth moment condition as the dominant population eigenvalues tend to infinity. Moreover, in the case of the maximum eigenvalue bounded, once the gap condition is satisfied, the rate of convergence to 1 is faster than that of AIC in the correct estimate probability, especially it performs better with a small sample size. It is worth noting that when finite fourth moment are not satisfied or there is a heavy-tailed distribution, the variance criterion significantly improves the accuracy of model selection compared with AIC.

 欢迎各位老师、学生届时参与！