Empirical Likelihood for Composite Quantile Regression Models with Missing Response Data

Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically χ2. Secondly, without an estimation of the asymptotic covariance, confidence intervals are constructed for the regression coefficients. Thirdly, three estimators are presented for the regression parameters to obtain its asymptotic distribution. The finite sample performance is assessed through simulation studies, and the symmetry confidence intervals of the parametric are constructed. Finally, the effectiveness of the proposed methods is illustrated by analyzing a real-world data set.