| It is a great challenge to deal with high dimensional data in practice.Sufficient dimension reduction is a class of methods to handle the high dimensional data.In sufficient dimension reduction,a small number of linear combinations of the original predictors are found and used to replace themselves without great loss of the regression information.Aggregate dimension reduction(ADR)is based on the fact that the central subspace can be decomposed into a finite number of local dimension reduction spaces,and the estimates of the local dimension reduction subspaces can be aggregated to obtain the estimate of the dimension reduction subspace.Aggregate inverse mean estimation(AIME)combines the idea of the aggregation and the cumulative mean estimation(CUME).This method uses the K-nearest neighbor algorithm to give the local areas,and in each of them,the dimension reduction is conducted.This method does not depend so much on the assumptions about the distribution of the predictors,and it is not sensitive to the type of regression function.Moreover,the exhaustivity of the aggregate inverse mean estimate for the central subspace is usually satisfying.As there are often outliers in practical data,which may have negative impact on the estimate of the dimension reduction subspace,we focus on assessing the impact of the observations on the dimension reduction results in this thesis.Based on the framework proposed by Chen et al.(2022),we propose a local influence analysis method for AIME.This method uses the space displacement function to measure the discrepancy between the central subspace estimates obtained before and after the perturbation is introduced.Based on the describe of the local behavior at the null perturbation point of the space displacement function,we can obtain the expression of quasi-curvature and find the influential direction for the estimates of the central subspace,which can be used as the influence assessment statistics.The proposed method is illustrated by a simulation study. |
