Local Influence Analysis In Groupwise Sufficient Dimension Reduction

Advances in modern computing power have made it possible to process massive amounts of data.However,as data information keeps increasing,it will become more and more difficult to use non-parametric methods to make statistical inferences on highdimensional data,which may lead to the "curse of dimensionality".Sufficient dimension reduction provides a feasible idea for solving such problems.Its basic idea is to find a small number of linear combinations of the original independent variables to replace them with the regression information preserved as much as possible.Till now,a variety of sufficient dimension reduction methods have been proposed.In practice,there may also be a large number of cases where the predictor can fall naturally into a number of groups according to their own characteristics.To handle these cases,it is feasible and popular to use the groupwise dimension reduction method,since this method can fully consider the prior group knowledge and have advantages in achieving better accuracy and interpretability of estimates.Since the inference result of sufficient dimension reduction is often used in the further study of high-dimensional nonparametric regression,it is necessary to study the sensitivity of sufficient dimensionality reduction method.In this thesis,a local influence analysis for the g-RMAVE method is proposed.This method relies on the space displacement function which is a function of the perturbation vector to describe the discrepancy between the dimension reduction subspace estimates obtained before and after the perturbation is introduced.Based on that,by constructing the lifted line along the direction h on the influence graph,the expression of the quasi-curvature is derived to measure the local influence of the small perturbation to the model on the dimension reduction subspace estimates,and then the method of finding the influential direction is given,which can be used as the assessment statistic of the local influence.To reduce the computational burden,we introduce the joint perturbations to data points only in the last iteration of the g-RMAVE algorithm.In addition,the proposed method is illustrated by a simulation study.The inference results in the simulation show that the proposed method of local influence analysis helps to avoid masking effect and performs well in the identification of the outliers.