讲座题目：A New Scope of Penalized Empirical Likelihood with  High-dimensional Estimating Equations

主讲人：西南财经大学常晋源教授 

讲座时间:2017年12月5日（星期二）3:00-4:00

讲座地点：浙江工商大学综合楼601会议室

主讲人简介：2005年9月至2009年7月，北京师范大学数学科学学院本科学习，2009年7月获理学学士学位（统计学专业）；2009年9月至2013年7月，北京大学光华管理学院硕博连读（师从陈松蹊教授），2013年7月提前取得经济学博士学位（统计学专业）；2013年9月至2017年2月，澳大利亚墨尔本大学数学与统计学院Research  Fellow（师从Peter Hall教授）；2017年3月至今，西南财经大学统计学院全职教师。2012年获国际数理统计协会Laha  Award，2013年获中国数学会钟家庆数学奖。现为统计学国际顶级学术期刊JRSSB和国际一流学术期刊Statistica Sinica的Associate  Editor。

摘要：

Statistical methods with empirical likelihood (EL) are  appealing and effective especially in conjunction with estimating equations  through which useful data information can be adaptively and flexibly  incorporated. It is also known in the literature that EL approaches encounter  difficulties when dealing with problems having high-dimensional model parameters  and estimating equations. To overcome the challenges, we begin our study with a  careful investigation on high-dimensional EL from a new scope targeting at  estimating high-dimensional sparse model parameters. We show that the new scope  provides an opportunity for relaxing the stringent requirement on the  dimensionality of the model parameters. Motivated by the new scope, we then  propose a new penalized EL by applying two penalty functions respectively  regularizing the model parameters and the associated Lagrange multiplier in the  optimizations of EL. By penalizing the Lagrange multiplier to encourage its  sparsity, a drastic dimension reduction in the number of estimating equations  can be effectively achieved without compromising the validity and consistency of  the resulting estimators. Most attractively, such a reduction in dimensionality  of estimating equations is actually equivalent to a selection among those  high-dimensional estimating equations, resulting in a highly parsimonious and  effective device for high-dimensional sparse model parameters. Allowing both the  dimensionalities of model parameters and estimating equations growing  exponentially with the sample size, our theory demonstrates that our new  penalized EL estimator is sparse and consistent with asymptotically normally  distributed nonzero components. Numerical simulations and a real data analysis  show that the proposed penalized EL works promisingly.