Random Weighting Quantile Regression For Linear Errors-in-variables Models

In the study of real data, the traditional linear regression model only considers the measurement error of the dependent variable, but does not consider the measurement error of the independent variable. The data obtained in reality are generally in error, which is easy to lead to the deviation of parameter estimation.The linear errors-in-variables model is the regression model with the measurement error, and corrects the deviation of the parameter estimation caused by the measurement error of the independent variable. The linear errors-in-variables model is more practical than the traditional linear regression model usually.Quantile regression is a robust estimation method developed based on the classical least square method, which can be a robust estimator even when least square method fails.The distribution of the random error is not assumed, the application is more relaxed and the model is robust when we use quantile regression. Quantile regression is a regression estimate of all the quantile points, so it is not sensitive to the outliers in the data. The information obtained is more abundant.In this paper, the random weighting method is extended to the linear errors-in-variables models. By combining the quantile regression, propose random weighting quantile regression for linear errors-in-variables models. Firstly, it is shown that the random weighting quantile regression estimation is uniformly consistent. Secondly, based on quantile regression estimation, we consider the test problem for the linear errors-in-variables model. This paper uses the random weighting method to establish the random weighted test statistic and carries on the linear hypothesis test. Finally, The simulation studies and an AIDS real data application are conducted to illustrate the finite sample performance of the proposed methods.The random weighting method provides a way of assessing the distribution of the quantile regression estimators without estimating the nuisance parameters.