With nonignorable dropouts and outliers, we propose robust statistical inference and variable selection methods for linear quantile regression models based on composite quantile regression and empirical likelihood (EL) that accommodate both the within-subject correlations and nonignorable dropouts. The purpose of our study is threefold. First, we apply the generalized method of moments to estimate the parameters in the nonignorable dropout propensity based on an instrument. Subsequently, the inverse probability weighting and kernel smoothing approaches are applied to obtain the smoothed and bias-corrected generalized estimating equations. Second, we borrow the idea of quadratic inference function to construct the improved EL procedure for nonignorable dropouts. The asymptotic properties of the proposed estimators and their confidence regions are derived. Third, the penalized EL method and algorithm for variable selection are investigated. The finite-sample performance of the proposed estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.

中文翻译：

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改进的复合分位数回归和具有不可忽略丢失的变量选择

对于不可忽略的辍学和异常值，我们提出了基于复合分位数回归和经验似然 (EL) 的线性分位数回归模型的稳健统计推断和变量选择方法，该方法同时适应了受试者内相关性和不可忽略的辍学。我们研究的目的有三个。首先，我们应用广义矩方法来估计基于工具的不可忽略辍学倾向中的参数。随后，应用逆概率加权和核平滑方法来获得平滑和偏差校正的广义估计方程。其次，我们借用二次推理函数的思想来构建改进的 EL 程序，用于不可忽略的 dropout。推导出了所提出的估计量及其置信区域的渐近特性。第三，研究了变量选择的惩罚EL方法和算法。通过仿真研究了所提出的估计器的有限样本性能，并提出了在 HIV-CD4 数据集上的应用。