主 题：Robustified Sure Independence Screening via Rank-Based Distance Correlation
主讲人：首都师范大学 崔恒建教授
主持人：林华珍教授
时 间：2014年7月22日下午4：00-5：00
地 点：通博楼B座212学术会议室
主办单位：统计学院 统计研究中心 科研处
主讲人简介：
崔恒建，首都师范大学教授，博士生导师，为国务院学位委员会学科评议组专家。在数理统计和稳健统计理论和方法、金融统计、遥感统计与质量管理等领域取得过许多骄人和杰出的研究成果，发表论文100余篇，其中包括发表在国际顶级的统计和计量经济学杂志《Annals of Statistics》、《Journal of Econometrics》、《Journal of the Royal Statistical Society B》和《Biometrika》上，主持或主研基金项目共计15项。崔恒建教授现任《应用数学学报》中、英文版编委、《数理统计与管理》编委、中国概率统计学会常务理事、中国现场统计学会理事，生存分析分会理事、国际泛华统计协会会员、美国数学会数学评论员、国际数理统计学会（中国分会）常务理事。曾获第六届中国科协期刊优秀学术论文三等奖（2009）、教育部高等学校科学技术奖--自然科学奖二等奖（2006）、第八届全国统计科学研究优秀成果奖一等奖（2006）、第八届全国统计科学研究优秀教学成果奖二等奖（2006）、北京师范大学科优秀科研成果奖（2002）、国家统计局全国统计科学技术进步二等奖（1998）、京津五四青年概率统计学术年会“盖洛普”奖（1997）
内容提要：
In this talk we propose a robustified sure independence screening (R-SIS) procedure by using the rank-based distance correlation as a marginal utility to perform feature screening. The existence of the rank-based distance correlation does not require any moment conditions for either the predictors x or the response Y. It thus allows both x and Y to have heavy-tailed distributions. The implementation of this R-SIS procedure also refrainscompletely from standardizing x. The standardization for x is often utilized in implementing other SIS procedures, which aims to make the magnitudes of the marginal utilities comparable in many existing SIS procedures. It may have an adverse effect however, when the second or even the first moment of x does not exist. In addition, the implementation of this R-SIS procedure does not assume parametric structures between x and Y either. It thus identifies the important predictors in a model-free manner. This is a very appealing property in ultrahigh dimensional settings, particularly when there is little information about the underlying true regression structure. We investigate the theoretical properties of this R-SIS procedure and establish both the sure screening and the ranking consistency property when the predictor dimension p diverges at the rate of o{exp(n^(1-2k)}, where n is the sample size and 0<= k < 1/2 controls the signal strength. This is the fastest possible rate of p that an SIS procedure can handle in theory. We demonstrate the performance of this R-SIS procedure through comprehensive simulations and a real data application.
