Statistical Inference for Partially Linear Varying Coefficient Quantile Models with Missing Responses

The construction of confidence intervals is investigated for the partially linear varying coefficient quantile model with missing random responses. Combined with quantile regression, an imputation-based empirical likelihood method is proposed to construct confidence intervals for parametric and varying coefficient components. Then, it is proved that the proposed empirical log-likelihood ratios are asymptotically Chi-square in theory. Finally, the symmetry confidence intervals of the parametric components and the point-by-point confidence intervals of the varying coefficient components are constructed in the simulation studies to demonstrate further that the proposed method yields smaller confidence intervals and higher coverage probabilities.