统计与管理学院2017年学术报告第78期
【主 题】 On condition number constrained estimation of precision matrix
【报告人】 Chunming Zhang, 教授
University of Wisconsin-Madison
【时 间】 2017年12月19日（星期二）14:10-14:50
【地 点】 上海财经大学统计与管理学院大楼1208会议室
【摘 要】Estimation of large precision matrices is fundamental to high-dimensional inference. We will discuss the estimation of the precision matrix by imposing a bound on the condition number of the estimate, which effectively ensures well-conditioning. Specifically, we propose a correlation-based estimator, constrained with both the condition number and the L1 penalty, yielding a precision matrix estimator with theoretically guaranteed rate of convergence. This result further enables us to demonstrate that incorporating the L1 penalty is necessary for achieving consistency of the resulting estimator in typical high-dimensional settings, while inconsistency will occur when the L1 penalty is absent. An algorithm is developed to implement the proposed method, which reveals the satisfactory performance in simulation studies. An application of the method to a call center data is illustrated.
