Research On Robust Variable Selection Problem Based On AME Estimation

In linear regression models,the optimal estimates for each distribution are different due to the diversity of error distributions.In this paper,the asymmetric exponential power distribution(AEPD)is used to obtain the normal distribution,the Laplace distribution,the generalized normal distribution and the asymmetric Laplace distribution by adjusting the parameters of the distribution.Therefore,the estimation method based on the AEPD can better adapt to various types of distribution data including special distribution.In this paper,the problem of robust variable selection is studied based on AEPD.The proposed method can not only ensure the robustness of the estimation under the error obeying various types of distribution,but also obtain better prediction results.In calculation,a new calculation method is provided,which uses the MM algorithm to calculate the initial value of the estimation.At the same time,the MM algorithm is used to solve the problem that the penalty item cannot be guided at 0.Finally,the goodness of the estimation proposed in this paper is verified by data simulation and empirical data analysis.