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）下昼2:00-3:00

Place (地 点)：北京大学理科一号楼1303课堂

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（报告人先容）：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，中国数学会普及事情委员会副主任，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《数理统计与治理》副主编。

研究偏向：统计质量控制(SPC)、半参数回归。已在焦点刊物上揭晓学术论文三十余篇，出书书一本。96年获第三届天下统计科学前进三等奖，99年获第五届天下统计科研优异效果二等奖，有一项基金项目被天津科委判断为“海内领先”水平。