基于切片逆回归的稳健降维方法

Robust Dimension Reduction Method Based on Sliced Inverse Regression

经典的充分降维方法对解释变量存在异常值或者当其是厚尾分布时效果较差,为此,经过对充分降维理论中加权与累积切片的分析研究,本文提出了一种将两者有机结合的稳健降维方法——累积加权切片逆回归法(CWSIR)。该方法对自变量存在异常值以及小样本情况下表现比较稳健,并且有效避免了对切片数目的选择。数值模拟结果显示CWSIR要优于传统的切片逆回归(SIR)、累积切片估计(CUME)、基于等高线的切片逆回归估计(CPSIR)、加权典则相关估计(WCANCOR)、切片逆中位数估计(SIME)、加权逆回归估计(WIRE)等方法。最后,通过对某视频网站真实数据的分析也验证了CWSIR的有效性。

Classical sufficient dimension reduction methods perform not well when the predictors contain outliers or the distribution of the predictors is heavy-tailed and therefore,after the analysis of weighting and cumulating slices in the framework of sufficient dimension reduction,this paper proposes a new method called cumulative weighted slice inverse regression,CWSIR for short,which is an organic combination of weighting and cumulating. Our proposed method is robust to the outliers existed in predictors and small sample size,and effectively avoids the choice of the number of slices. The simulation results show that CWSIR is superior to other existing traditional approaches,such as Sliced Inverse Regression（ SIR）,Cumulative Mean Estimation（ CUME）, Contour Projection of Sliced Inverse Regression（ CPSIR）, Weighted Canonical Correction（ WCANCOR）,Slices Inverse Median Estimation（ SIME） and Weighted Inverse Regression Estimation（ WIRE）. Finally,the real data analysis of video data also verifies the efficiency of our method.