统计学系系列讲座之299期

时间：2018年5月17日（周四）16:00-17:00

地点：李达三楼104室

主持人：朱仲义  教授 复旦大学管理学院统计学系

主题：From Multiple Gaussian Sequences to Functional Data: A Stein Estimation Approach

主讲人：姚方 教授  多伦多大学

简介：姚方，多伦多大学统计科学系教授，北京大学讲席教授，国家“**计划”入选专家。主要研究方向包括无限维空间的函数型数据分析， 现阶段的研究集中在具有高维或者流形结构的函数型数据的方法和理论以及在大型复杂数据中的应用。2014年获得由加拿大统计学会和数学研究中心联合颁发的授予博士毕业15年内在加拿大做出突出贡献的统计学家的 CRM-SSC奖，2017年当选为国际数理统计学会（IMS）Fellow。担任十个国际统计学核心期刊的副主编，包括顶级期刊Journal of the American Statistical Association和 Annals of Statistics。

摘要：We expand the notion of Gaussian sequence model to n experiments and propose a Stein estimation strategy which relies on pooling information across experiments.  An oracle inequality is established to assess conditional risks given the underlying effects, based on which we are able to quantify the size of relative error and obtain a tuning-free recovery strategy that is easy to compute, produces model parsimony and extends to unknown variance.  We show that the simultaneous recovery is adaptive to an oracle strategy, which also enjoys a robustness guarantee in a minimax sense.  A connection to functional data is established, via Le Cam theory, for fixed and random designs under general regularity settings.  We further extend the model projection to general bases with mild conditions on correlation structure, and conclude with potential application to other statistical problems. Simulated and real data examples are provided to lend empirical support to the proposed methodology and illustrate the potential for substantial computational savings.

                                                           统计学系 

2018-5-16