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数学学院、所2019年系列学术活动(第159场):常晋源教授 西南财经大学

发表于: 2019-09-19 14:59  点击:

报告题目:Optimal Covariance Matrix Estimation for High-dimensional Noise in High-frequency Data

报 告 人:常晋源教授 西南财经大学

报告时间:2019920日下午1400-1500

报告地点:数学楼629

报告摘要:

In this paper, we consider efficiently learning the structural information from the high dimensional noise in high-frequency data via estimating its covariance matrix with optimality. The problem is uniquely challenging due to the latency of the targeted high-dimensional vector containing the noises, and the practical reality that the observed data can be highly asynchronous – not all components of the high-dimensional vector are observed at the same time points. To meet the challenges, we propose a new covariance matrix estimator with appropriate localization and thresholding. In the setting with latency and asynchronous observations, we establish the minimax optimal convergence rates associated with two commonly used loss functions for the covariance matrix estimations. As a major theoretical development, we show that despite the latency of the signal in the high-frequency data, the optimal rates remain the same as if the targeted high-dimensional noises are directly observable. Our results indicate that the optimal rates reflect the impact due to the asynchronous observations, which are slower than that with synchronous observations. Furthermore, we demonstrate that the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. We also illustrate the empirical performance of the proposed estimator with extensive simulation studies and a real data analysis.

报告人简介:

常晋源教授20137月在北京大学取得博士学位,之后前往澳大利亚墨尔本大学数学与统计学院从事博士后研究,师从已故国际统计学泰斗Peter Hall教授,20173月全职回到西南财经大学统计学院工作。现为西南财大—电子科大—四川省统计局—四川移动数据科学与商业智能联合实验室执行主任、四川省特聘专家,是国家青年“QR计划”特聘专家和教育部青年长江学者。常晋源教授主要从事超高维数据分析、经验似然方法及其应用、以及金融计量经济学三方面的研究,并取得了一些重要科研成果。先后以第一作者在《Annals of Statistics》《Biometrika》《Biometrics》和《Journal of Econometrics》等统计学与计量经济学国际顶级学术期刊发表论文十余篇。担任《Journal of the Royal Statistical Society Series B》《Journal of Business & Economic Statistics》《Statistica Sinica》等统计学杂志的副主编。20124月获得国际数理统计协会(Institute of Mathematical StatisticsLaha Award,这是中国大陆高校培养博士中的首位获奖者,201310月获得第十一届钟家庆数学奖。