Study On Estimation Of Quantile Regression Models With Measurement Error

The problem of measurement error is common in many fields,such as economics,medicine,financial.For example,in medical and biological statistics,the predictive variables were usually measured with error and thus the estimation of parameters based on the traditional method is biased.As one of the most important method on regression research,the quantile regression model is widely used in medical,economic,financial,environmental and other fields.It is mainly used in the establishment of medical reference intervals,survival analysis,market risk measurement,environmental simulation and heteroscedasticity detection.This paper mainly deals with the estimation of quantile regression models with measurement errors.Firstly,the quantile regression model and the measurement error model are introduced respectively,and the influence of measurement error on the parameter estimation of mean regression model is introduced.Taking the instrumental variable method as an example,the parameter estimation method of mean regression model with measurement error is given in detail.Secondly,the factor score method for mean regression model with measurement error is introduced.Based on this method,the corrected factor score(CFS)method is proposed to solve the problem of measurement error in linear quantile regression model.Then,the stochastic simulation is carried out,and the corrected factor score estimation and the orthogonal regression estimation are compared.The result shows that the CFS method is asymptotically unbiased when the error obeys the normal distribution.Finally,the simulation extrapolation(SIMEX)method is introduced and applied to the parametric and the nonparametric quantile regression model with measurement error.Through the random simulation,we conclude that the SIMEX method can correct the deviation in estimation caused by the measurement error of different models.In general,the CFS method can be easily used to estimate the parameter of linear quantile regression model.As a supplement to the former,the SIMEX method can not only solve the estimation problem of linear or parametric quantile regression model,but also solve the estimation problem of nonlinear or nonparametric quantile regression model.