Induced Smoothing Estimator For Quantile Regression Model With Panel Data

In this paper,the idea of induced smoothness is introduced into the quantile regression model of panel data.In the fixed effect model,the point estimation and the asymptotic confidence interval estimation of regression parameters are constructed simultaneously.Because there are unknown parameters in the asymptotic variance of classical estimation methods,it is difficult to obtain an effective confidence interval estimation.A new method,induced smooth estimation,is introduced in this paper,and the estimation algorithm is given.Then,Monte Carlo experiments are carried out to compare the efficiency of the new method and the least square method,the estimation of quantile regression model(LAD estimation)and the estimation of the shortest distance of quantile regression under limited samples.Finally,the empirical analysis of two real data shows that the induced smoothing method has certain advantages in parameter estimation of panel data quantile regression model.The work of this paper is divided into the following aspects:(1)For the panel data quantile regression model,a smoothing function is constructed to obtain the point estimation of the parameters of the panel data quantile regression model.The estimation efficiency of different methods is verified by Monte Carlo simulation.(2)In the fixed-effect panel data quantile regression model,the asymptotic confidence interval of the shortest distance estimation(MDQR)is constructed based on the induced smoothing method.It is found that the new method has shorter confidence interval length and higher prediction accuracy.(3)Empirical analysis,this paper applies induced smoothness estimation method to empirical analysis,and obtains effective confidence interval and parameter estimation in empirical analysis,which shows that the length of confidence interval obtained by induced smoothness estimation is shorter and the effect is better.