Local Influence Analysis Based On Objective Function For DMAVE Method In Sufficient Dimension Reduction

In the era of big data,we often use high-dimensional data,and sufficient dimension reduction can retain the information of original data to the maximum extent.However,dimension reduction methods relies heavily on the original data,so it is necessary to analyze the influence of the observed data.Minimum average(conditional)variance estimation based on density function(d MAVE)is a very important method for sufficient dimension reduction.This paper proposes a local influence analysis method for d MAVE.This method relies on a space displacement function that measures the distance between the dimension reduction space with and without model perturbation.By introducing joint perturbation,the theoretical system of local influence analysis based on d MAVE objective function is constructed,and local influence assessment statistic is obtained to evaluate the influence of all sample on the estimated central dimension reduction subspace.In order to obtain the influence assessment statistic in this system,this paper introduces the constraint of dimension reduction vector to construct the Lagrange function based on the traditional d MAVE objective function,so as to get rid of the dependence of d MAVE iterative algorithm.Simulation results show that the local influence analysis based on objective function for d MAVE performs well,and can process the data with "masking" effect and identify outliers successfully.