报告题目：Variance Variation Criterion and Consistency in Estimating the Number of Significant Signals of High-dimensional PCA
时 间：2022年11月14日（星期一）上午14：30-15：30
地 点：腾讯会议（688-215-099）
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
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.
报告人简介：现为首都师范大学教授，博士生导师，中国科协第十届全委会委员，曾任国务院学位委员会学科评议组专家。中国科学院系统科学研究所博士毕业。在大数据统计建模、高维统计及其稳健统计理论和方法、统计机器学习、金融统计、以及质量管理等领域取得过许多重要的研究成果，发表论文180余篇，其中包括发表在国际顶级的统计和计量经济学杂志JASA、AoS、JRSS(B)、Biometrika和JoE上。主持国家自然科学基金重点项目、杰青（B）项目以及多项面上项目、主要参加教育部重大科研基金项目、科技部863等项目。现担任《数学学报》和《应用数学学报》中、英文版以及《Statistical Theory and Related Fields》编委，中国现场统计研究会副理事长，全国工业统计教育研究会副理事长，北京应用统计学会会长，国际数理统计学会（中国分会）常务理事。曾获得教育部高等学校科学技术奖-自然科学奖二等奖；全国统计科学研究优秀成果奖一等奖等。