科学研究

邱宇谋，博士毕业于爱荷华州立大学，先后在内布拉斯加林肯大学和爱荷华州立大学任教。于2023年7月加入北京大学数学科学学院、统计科学中心，职位为长聘副教授。他的研究包括高维数据分析、高维协方差矩阵和精度矩阵的统计推断、因果分析、缺失数据分析。同时，他也致力于统计方法在精准农业、流行病模型、法医学等领域的应用研究。

This talk considers testing for high dimensional covariance and precision matrices by deriving the detection boundaries as a function of the signal sparsity and signal strength. It first shows that the optimal detection boundary for testing sparse means is the minimax detection lower boundary for testing covariance and precision matrices. Multi-level thresholding tests are proposed and are shown to be able to attain the detection lower boundaries over a substantial range of the sparsity parameter, implying that the multi-level thresholding tests are sharp optimal in the minimax sense over the range. The asymptotic distributions of the multi-level thresholding statistic for covariance and precision matrices are derived by developing a novel U-statistic decomposition to handle the complex dependence among the elements of the estimated covariance and precision matrices. The superiority in the detection boundary of the multi-level thresholding test over the existing tests are also demonstrated.