MM-Algorithm For Estimating A Class Of Variational Coefficient Quantile Regression Models

In this paper,the variable-coefficient quantile regression model is obtained by combining the variable-coefficient quantile regression model with the quantile regression model,which has strong flexibility,interpretability and robustness.Aiming at the variational coefficient quantile regression model,this paper introduces MM(Majorization Minimization)algorithm into the estimation problem of variational coefficient quantile regression model,and proposes a new linear estimation method:local linear estimation method based on MM algorithm.The basic principle of MM algorithm is:firstly,we find the replacement function of the objective function of the variable coefficient model and simplify the complex objective function.Secondly,based on the minimization process of the replacement function,we gradually iterate to obtain the optimal solution of the replacement function,which is the approximate solution of the objective function,and then obtain the estimated value of the coefficient function.We choose two variable coefficient quantile regression model,in view of the different variables distribution random sample data and numerical simulation,get the estimate,and then select the deviation value(Bias),mean absolute error(MAE),mean square error(MSE)and root mean square error(RMSE)of the four basic index to evaluate the accuracy of estimation.The experimental results show that the four evaluation indexes of the local linear estimation method based on the MM algorithm fluctuate between 0.01 and 0.3,while the four evaluation indexes of the common local linear estimation method fluctuate between 0.1 and 0.95.The numerical results verify that the local linear estimation method based on the MM algorithm has better stability.The estimation effect is better than the common local linear estimation method and the estimation accuracy is higher.Finally,the model is fitted with Boston housing price data to verify the practicality of the model in solving practical problems.