报告题目：Optimal sequence or ordinary sequence? A unified framework for variance estimation in nonparametric regression

报告时间：2016年12月26日下午16：00

报告地点：英国威廉希尔公司504室

报告人:童铁军教授(香港浸会大学数学系)

报告人简介：童铁军教授，主要研究方向包括非参数和半参数回归，高维数据分析，生物统计和整合分析。童教授于2005年在University of California at Santa Barbara获得统计学博士学位，2005-2007年在Yale University从事生物统计博士后研究，2007-2011年执教于University of Colorado at Boulder当助理教授，2011至今执教于香港浸会大学数学系。迄今为止,在国际著名的统计学期刊《JASA》、《Bioinformatics》、《Biometrics》、《Biometrika》、《Biostatistics》、《JMLR》、《Bernoulli》、《Statistica Sinica》等上发表学术论文40多篇。

目前在香港正承担多个政府和学校的科研基金项目，同时主持国家自然科学基金面上项目。

Abstract:Difference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this paper, we propose a unified framework for variance estimation that combines the linear regression method with the higher-order difference estimators systematically. The unified framework has greatly enriched the existing literature on variance estimation that includes most existing estimators as special cases. More importantly, the unified framework has also provided an ingenious way to solve the challenging difference sequence selection problem that remains a long-standing controversial issue in nonparametric regression for several decades. Using both theory and simulations, we recommend to use the ordinary sequence in the unified framework, no matter if the sample size is small or if the signal-to-noise ratio is large. Finally, to cater for the demands of the application, we have developed a unified R package that integrates the existing difference-based estimators and the unified estimators in nonparametric regression and will make it freely available in the R statistical program http://cran.r-project.org/web/packages/.