Random Weighted Composite Quantile Regression For Linear Errors-in-variables Models

Since measured data always have random error in reality applications,the linear errors-in-variables model with random error are more accord with reality situation.We usually use least square method to study the model,but in some situations it will fails.Composite quantile regression is a robust estimation method,which can be a robust estimator when least square method fails,and the relative efficiency of the composite quantile regression estimator compared with the least squares estimator is greater than 70% regardless of the error distribution.For normal errors,the asymptotic efficiency of composite quantile regression estimator compared with the least squares estimator is greater than 95.5%,and is greater than 100% with non-normal errors.Therefore,we take the idea of composite quantile regression to study linear errors-in-variables model.In Section two,we study the parameter estimation of the linear errors-in-variables model.The expression of the estimator and the asymptotic distribution are generally related to quantities of the error distribution that can not be conveniently estimated.The random weighting method is one method of solution the above problems.In this paper,we consider the random weighted composite quantile regression in linear errors-in-variables models.The random weighted method is used to approximate the distribution of the composite quantile regression,and it is demonstrated that the approximation is asymptotically valid with probability one.Finally,simulated examples are given to illustrate the performance of the proposed method.In Section three,based on random weighting composite quantile regression,we propose a test method to deal with the testing problem of the parameter in the linear errors-in-variables models under the null hypothesis.The critical values of the test statistic can be obtained by the random weighting method without estimating the nuisance parameters.Extensive simulations as reported,showing that the proposed method works well in practical settings.