Semiparametric Functional Coefficient Quantile Regression And Its Two-step Estimation Procedure

At present, semiparametric model, functional coefficient and quantile regression are key issues in the field of regression analysis.Koenker and Bassett proposed a famous linear quantile regresion which solves heavy tail problems effectively in 1970s. But in application, the model can not catch a more complicated quantile structure, such as nolinear or interactive relationships among variables. Then researchers propose nonparametric quantile regressions to get more information. However, nonparametic quantile regression can not catch the linear relationship among variables.In this paper, we propose a new semiparametric quantile regression, based on reveiews of semiparametric model, functional coefficient and quantile regression. Semiparametric quantile regression contains linear and nonlinear part simultaneously, it not only observes complicated realtionship among variables, but also discovers detailed movement for each variable. We also propose a new two-step estimation procedure to estimate the semiparametric quantile regression. Because traditional profile least square is invalid for nonliearity of quantile regression. To estimate the constant parameters in the model, first, the constant coefficients are regarded as functional coefficients and then we apply a nonparametric estimation procedure. The final estimators of those parameters are obtained by the average method. To estimate the functional coefficents optimally, we simple use the partial residuals, then apply a nonparametic estimation procedure.Finally, we take a famous boston housing prices data as an example to show the power of semiparametric quantile model and its two-step estimation in application.