Quantile regression and smoothed empirical likelihood for non-ignorable missing data based on semi-parametric response models

This is the authors' abstract. We don't add key points for this paper.

In the context of quantile regression with non-ignorable missingness in the response variable, we introduce a semi-parametric exponential tilting model that captures the missingness propensity. To address this, we propose three convolution smoothing-based estimators for quantile regression: inverse probability weighting (IPW), estimation equation imputation (EEI), and augmented IPW (AIPW). These estimators provide consistent estimates for quantile regression coefficients, utilizing the framework of empirical likelihood. We establish theoretical results regarding the asymptotic normality of the three quantile regression estimators, as well as the chi-square 性质 of the corresponding adjusted logarithmic empirical likelihood ratios. Furthermore, we conduct numerical simulations to evaluate the finite-sample performance of these estimators, demonstrating their robustness. To further illustrate the effectiveness of the proposed methods, we apply them to HIV-CD4 data. This application allows us to investigate the differential impact of missing data mechanisms across treatment groups and explore the influence of baseline and previous CD4 and CD8 cell levels on current CD4 cell levels.