Title (题 目)：Local Walsh Average Regression

Speaker (报告人)：Professor Zhaojun Wang, 王兆军教授

南开大学数学科学学院统计系主任

Time (时 间)：2010年9月16日（周四）下午2:00-3:00

Place (地 点)：北京大学理科一号楼1303教室

Abstract (摘要)：Local polynomial regression is widely used for nonparametric regression. However, the efficiency of least squares (LS) based methods is adversely affected by outlying observations and heavy tailed distributions. On the other hand, the least absolute deviation (LAD) estimator is more robust, but may be inefficient for many distributions of interest. Kai, Li and Zou (2010) propose a nonparametric regression technique called local composite quantile regression (LCQR) smoothing to improve local polynomial regression further. However, the performance of LCQR depends on the choice of the number of quantiles to combine, a meta parameter which plays vital roles in balancing the performance of LS and LAD based methods. To overcome this issue, we propose a novel method termed the local Walsh-average regression (LWAR) estimator by minimizing a locally Walsh-average based loss function. Under the same assumptions in Kai, Li and Zou (2010), we theoretically show that the proposed estimator is highly efficient across a wide spectrum of distributions. Its asymptotic relative efficiency with respect to the LS based method is closely related to that of the signed-rank Wilcoxon test in comparison with the $t$-test. Both of the theoretical and numerical results demonstrate that the performance of the new approach and LCQR is at least comparable in estimating nonparametric regression function or its derivatives and in some cases the new approach performs better than the LCQR with commonly recommended number of quantiles, especially for estimating the regression function. Besides, the minimization algorithm for LWAR is much faster because it has much less parameters. \vspace{0.2cm} \noindent{{\bf Keywords:} Asymptotic efficiency; Local composite quantile estimator; Local polynomial regression; Robust nonparametric regression; Walsh-average regression}

About the speaker（报告人介绍）：王兆军教授，南开大学数学科学学院统计系主任，天津市数学会秘书长，天津市现场统计研究会副理事长，中国数学会理事，中国数学会普及工作委员会副主任，中国概率统计学会常务理事，中国现场统计研究会理事，杂志《数理统计与管理》副主编。

研究方向：统计质量控制(SPC)、半参数回归。已在核心刊物上发表学术论文三十余篇，出版书一本。96年获第三届全国统计科学进步三等奖，99年获第五届全国统计科研优秀成果二等奖，有一项基金项目被天津科委鉴定为“国内领先”水平。