Local Influence Analysis Of Sufficient Dimension Reduction For Multivariate Response Data

The dimension reduction of high-dimensional data has become an important issue in the area of nonparametric regression.The sufficient dimension reduction replaces the predictors by a small number of their linear combinations with as small loss of regression information as possible.The sufficient dimension reduction is needed for not only the models with single response but also the ones with multiple responses,as the data to be processed become larger and larger and the problems under study become more and more complex,which makes it particularly important to reduce the data dimension and construct a concise and effective model.Since many sufficient dimension reduction methods rely heavily on distributional assumptions of predictors,it is necessary to conduct influence analysis of the observations.The estimation of the kth moment dimension reduction subspace under multi-response model is a very important method of sufficient dimension reduction.In this thesis,a local influence analysis method for the estimate of the kth moment dimension reduction subspace under multi-response model is proposed.This method is based on the space displacement function,which is used to measure the discrepancy between the estimates of dimension reduction subspace before and after model perturbation.We construct a theoretical system of local influence analysis for the estimate of the kth moment dimension reduction subspace under multi-response model,in which we perturb the data jointly and assess the influence of all the observations on the estimate of the dimension reduction subspace by the local influence assessment statistics.Simulated examples are used to illustrate the proposed methodology,where the proposed method can avoid masking effect and identify outliers.