Expectile Regression With Errors-in-variables

Due to the imperfection of tools or the influence of human factors,errors often occur between observed data and real data.Therefore,measurement error models are widely used in various fields such as engineering,finance,biology and medicine.Regression model is a statistical model to study the quantitative relationship between variables.We can establish a regression model of observed data for testing,forecasting and a series of statistical inferences.If the measurement error of observed data is ignored directly,the estimation of parameters in the regression model will be biased and inconsistent.Therefore,it is of great practical significance and research value to explore how to reduce the deviation caused by measurement error.Linear measurement error models can directly obtain uniformly optimal linear unbiased estimators by minimizing the sum of squares of residuals,but it is difficult to directly obtain the unbiased estimators of expectile regression with errors-in-variables model.Therefore,we construct the expectile regression with errors-in-variables model by using the method of orthogonal distance regression to obtain parameter estimators.In the case of large samples.The asymptotic normality of the estimator is proved.Then,the weighted iterative least squares algorithm(IRWLS)is selected as the algorithm to solve the model.Next,through a large number of simulation experiments,the expectile regression with errors-in-variables,the quantile regression with errors-in-variables,and the differences between the traditional quantile regression and linear regression are compared and analyzed,and the effectiveness of the expectile regression with errors-in-variables model proposed in this paper is verified in reducing the deviation caused by the measurement error.Finally,the proposed model was applied to ACTG315 data set to study the relationship between HIV viral load and CD4+T cell number in AIDS patients,and was compared with other methods to further illustrate the effectiveness and accessibility of expectile regression with errors-in-variables model proposed in this paper.Finally,the correlative parameter estimation results and corresponding confidence intervals are given.