主 题：Band Width Selection for High Dimensional Covariance Matrix Estimation
主讲人：陈松蹊教授
主持人：常晋源博士
时 间：2015年5月18日下午2：30-3：30
地 点：通博楼B212学术会议室
主办单位：统计研究中心 统计学院 科研处
主讲人简介：
陈松蹊，美国爱荷华州立大学统计系教授，北京大学讲席教授，商务统计与经济计量系联合系主任、北京大学统计科学中心联席主任。他是国家首批“****”入选者，数理统计学会(Institute of Mathematical Statistics) 资深会员（fellow)，美国统计学会会士（fellow），国际统计学会 (International Statistics Institute) 当选会员 （elected member）。他现在是The Annals of Statistics(统计年鉴) 副主编；Journal of Business and Economic Statistics 副主编；以及Statistics and Its Interface 的联席主编。陈松蹊教授迄今已在国际权威学术杂志发表论文73篇，其中在JASA、JRSSB、 Annals of Statistics、Biometrika、Biometrics发表期刊29篇。
内容提要：
The banding estimator of Bickel and Levina (2008a) and its tapering version of Cai, Zhang and Zhou (2010) are important high dimensional covariance estimators. Both estimators require a band width parameter. We propose a band width selector for the banding estimator by minimizing an empirical estimate of the expected squared Frobenius norms of the estimation error matrix.
The ratio consistency of the band width selector is established. We provide a lower bound for the coverage probability of the underlying band width being contained in an interval around the band width estimate. Extensions to the band width selection for the tapering estimator and threshold level selection for the thresholding covariance estimator are made. Numerical simulations and a case study on sonar spectrum data are conducted to demonstrate the proposed approaches.
