1、Profile forward regressionscreening for ultra-high dimensional semiparametric varying coefficientpartially linear models
2、SIMEX estimation for single-indexmodel with covariate measurement error
报告时间：
1、2017年9月21日下午16：00
2、2017年9月22日上午9：00
报告地点：
1、科学会堂A602
2、科学会堂A710
报告摘要：
1、Inthis paper, we consider semiparametric varying coefficient partially linearmodels when the predictor variables of the linear part are ultra-highdimensional where the dimensionality grows exponentially with the sample size.We propose a profile forward regression (PFR) method to perform variablescreening for ultra-high dimensional linear predictor variables. The proposedPFR algorithm can not only identify all relevant predictors consistently evenfor ultra-high semiparametric models including both nonparametric andparametric parts, but also possesses the screening consistency property. Todetermine whether or not to include the candidate predictor in the model ofselected ones, we adopt an extended Bayesian information criterion (EBIC) toselect the ‘‘best’’ candidate model. Simulation studies and a real data exampleare also carried out to assess the performance of the proposed method and tocompare it with existing screening methods.
2、In this paper, we consider the single-indexmeasurement error model with mismeasured covariates in the nonparametric part. Tosolve the problem, we develop a simulation-extrapolation (SIMEX) algorithmbased on the local linear smoother and the estimating equation. For theproposed SIMEX estimation, it is not needed to assume the distribution of theunobserved covariate. We transform the boundary of a unit ball to the interiorof a unit ball by using the constraint $\|\beta\|=1$. The proposed SIMEXestimator of the index parameter is shown to be asymptotically normal undersome regularity conditions. We also derive the asymptotic bias and variance ofthe estimator of the unknown link function. Finally, the performance of theproposed method is examined by simulation studies and is illustrated by a realdata example.
报告人简介：
李高荣，北京工业大学教授，博士生导师。主要研究方向是复杂高维数据分析、深度学习、模型和变量选择、非参数统计、经验似然、纵向数据和测量误差模型等。于2007年7月在北京工业大学应用数理学院获得概率论与数理统计专业博士学位，2007年8月到2009年6月在华东师范大学金融与统计学院从事博士后研究工作，2016年3月到2017年3月为美国南加州大学Marshall商学院博士后。迄今为止，在《The Annals ofStatistics》、《Statisticsand Computing》、《Journalof Multivariate Analysis》、《StatisticaSinica》和《ComputationalStatistics and Data Analysis》等国内外重要学术期刊发表学术论文70多篇，其中40多篇发表在国际SCI期刊，在科学出版社出版专著《纵向数据半参数模型》和《现代测量误差模型》。目前主持国家自然科学基金、北京市自然科学基金和北京市教委科技计划面上项目。入选北京市属高等学校人才强教深化计划“中青年骨干人才培养计划”和北京市优秀人才培养资助计划和北京工业大学“京华人才”。
（数学与计算机科学学院、科技处）
