学术报告
报告题目：Optimal sequence or ordinary sequence? A unified framework for variance estimation in nonparametric regression
报告人：童铁军 副教授，香港浸会大学 数学系
报告时间：2015年4月28日 下午14:00—15:00
报告地点：研教楼409
报告校内联系人：王晓光 84708351-8123
报告摘要：Difference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this talk, we propose a unified framework for variance estimation that combines a recent regression technique with higher-order difference sequences 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. Two real data examples are also analyzed to demonstrate the practical usefulness of the unified framework. Finally, to cater for the demands of the application, we develop a unified R package that integrates the existing difference-based estimators and the unified estimators in nonparametric regression.
报告人简介：Tiejun Tong got Ph.D in Statistics, University of California at Santa Barbara in 2005. Now he is Associate Professor at Department of Mathematics Hong Kong Baptist University. His current research interests include Nonparametric and Semiparametric Regression, Shrinkage Estimation, High-Dimensional Data Analysis, Meta-Analysis.
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大连理工大学数学科学学院
统计与金融研究所
2015年4月22日
