Statistical Inference of Mode Regression with Adaptive Lasso

In this paper, an adaptive Lasso mode regression model is proposed to solve the problem of variable selection in mode regression model. Compared with the traditional mean regression and median regression, mode regression is robust when the distribution is heavy-tail or asymmetric. Kernel estimation is widely used in mode regression. When coping with high dimension, the method will result in calculation errors that hard to ignore. In this paper, the adaptive Lasso penalty is added to estimated parameters based on the mode regression model of the kernel estimation method, and the independent variables with low contribution rate are effectively eliminated. Therefore, the method can improve the accuracy of the calculation. The calculation method is described in detail in this paper, and this paper proposes the estimation methods of the parameters of the model and the asymptotic normality of the estimated values under some regular conditions. The simulation experiment and empirical analysis are performed to investigate the properties of the proposed method in finite sample. Compared with the traditional mode regression model and the mean regression model, the mode regression model with adaptive Lasso penalty greatly improves the accuracy of parameter estimation.