Statistical Inference For The Composite Quantile Regression Model Based On Empirical Likelihood With Missing Covariates

The composite quantile regression proposed by Zou and Yuan can provide efficient estimators via quantile regressions.Compared to the maximum likelihood,it does not assume the error distribution,which is generally unknown.The composite quantile regression can provide better estimators than the ordinary least squares in the presence of heavy-tailed distributions.By combining information over different quantiles via the criterion or loss function,the composite quantile regression can potentially improve estimation efficiency.Therefore,more and more attention has been paid to the method in recent years.In the statistical research,the phenomenon of missing data can be seen everywhere,which poses great challenges for statistical analysis.In such situations,one may discard completely the subjects with incomplete information.This method is known as complete-case analysis.This method is simple but may create bias and reduce efficiency of the parameter estimates,depending on the missing mechanism.This paper proposes an empirical likelihood-based weighted composite quantile regression approach for estimating regression parameters in linear model when some covariates are missing at random,and proves the large sample properties of the proposed estimator.The proposed estimator is computationally simple and more efficient than the inverse probability weighted estimator.Simulation studies further demonstrate the excellent properties of the new estimator under the limited samples,which agrees with our theory.The paper is organized as follows: The first chapter is introduction.The second chapter discusses the inverse probability weighted composite quantile regression method based on inference.In the third chapter we propose the weighted composite quantile regression based on empirical likelihood.Simulation studies and numerical comparisons are given in the fourth chapter.The fifth chapter gives the conclusion.