报告人：赵俊龙
报告地点：数学与统计学院五楼科学报告厅（501室）
报告时间：2015年12月09日星期三10:00-10:45
主讲人简介：
赵俊龙，副教授，北京航空航天大学数学与系统科学学院。目前主要研究方向：高维数据降维和变量选择，统计学习理论。 2007年4月博士毕业于北京理工大学理学院应用数学系。到北京航空航天大学数学与系统科学学院任教至今，曾为本科生主讲高等数学，概率论与数理统计等课程；为研究生主讲高等概率论，高等数理统计等课程。
报告摘要：
To estimate the high dimensional covariance matrix, row sparsity is often assumed such that each row has a small number of nonzero elements. However, in some applications, such as factor modelling, there may be many nonzero loadings of the common factors. The corresponding variables are also correlated to one another and the rows are nonsparse or dense. This paper has three main aims. First, a detection method is proposed to identify the rows that may be nonsparse, or at least dense with many nonzero elements. These rows are called dense rows and the corresponding variables are called pivotal variables. Second, to determine the number of rows, a ridge ratio method is suggested, which can be regarded as a sure screening procedure. Third, to handle the estimation of high-dimensional factor models, a two-step procedure is suggested with the above screening as the first step. Simulations are conducted to examine the performance of the new method and a real dataset is analyzed for illustration.
