简介：常晋源，西南财经大学数据科学与商业智能联合实验室执行主任、教授、博士生导师，主要从事“超高维数据分析”和“高频金融数据分析”两个领域的研究。已在统计学与计量经济学国际顶级学术期刊Annals of Statistics、Biometrika、Journal of Econometrics等上发表论文10余篇。现正担任Journal of the Royal Statistical Society Series B、Journal of Business & Economic Statistics和Statistica Sinica的Associate Editor，以及《应用概率统计》的编委。

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.