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# 讲座信息

20171124 常晋源：A New Scope of Penalized Empirical Likelihood with High-dimensional Estimating Equations

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.

20059月至20097月，北京师范大学数学科学学院本科学习，20097月获理学学士学位（统计学专业）；20099月至20137月，北京大学光华管理学院硕博连读（师从陈松蹊教授），20137月提前取得经济学博士学位（统计学专业）；20139月至20172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）；20173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 Award2013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 SinicaAssociate Editor