Sufficient Dimension Reduction Based On Model Averaging

Sufficient dimension reduction is an important issue in the field of nonparametric regression.The main purpose is to reduce the dimension of the independent variables and by finding a small number of linear combinations of independent variables,replace the original variable with these linear combinations without losing valid information.In various sufficient dimension reduction methods,all by estimating the kernel matrix and then take the eigenvector corresponding to the larger eigenvalue and reduce the dimension of the original data by corresponding eigenvector.In this paper discusses a sufficient dimension reduction method based on model averaging.Compared with the traditional sufficient dimensional reduction method,we don't use eigenvalue decomposition,but estimate the kernel matrix by the classical sufficient dimension reduction method,and then equate the problem of estimating central dimension reduction subspace with the problem of solving the minimum value problem of the objective function,and then solve the objective function iteratively by the model average method,come to estimate the central dimension reduction subspace..This objective function is applicable to most classical sufficient dimension reduction methods,and the precision of estimating the dimensionality reduction subspace can be improved by introducing model averaging methods.This paper adopts Mallows model averaging and Jackknife model averaging as the method basis.We conducted simulation experiments on a variety of models and used the trace correlation coefficient as our evaluation metric.We compare model based averaging algorithm with classical sufficient dimension reduction method.We use three kernel matrix estimation methods,which are Slice Inverse Regression,Slice Average Variance Estimation and Direction Regression.In most cases of simulation,model based averaging algorithm is better than classical sufficient dimension reduction method.At the same time,we explored the influence of the changes in data volume n and dimension p on dimension reduction effect of this algorithm.It is found that model average method is more suitable for the case where the data volume n is small and the dimension p is large.In this case,model based averaging algorithm is significantly better than classical sufficient dimension reduction method.Meanwhile performance results of the algorithms based on different model averaging methods are different.In a variety of models,the method based on Mallows model averaging is better than the method based on Jackknife model averaging.