统计与管理学院2016年学术报告第6期
【主 题】The effect of L1 penalization on condition number constrained estimation of precision matrix
【报告人】 郭潇
中国科学技术大学
【时 间】 2016年3月25日（星期五）15:30－16:30
【地 点】 上海财经大学统计与管理学院大楼1208室
【摘 要】 Estimation of large precision matrices is fundamental to high-dimensional inference. An important issue is to deal with ill-conditioning of the precision matrix estimate, typically encountered in finite-samples, but was rarely studied in the literature. In this paper, we focus on estimating 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 based on the alternating direction method of multipliers 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.
【邀请人】 冯兴东
