The kth ($1<k\le 2$) power expectile regression (ER) can balance robustness and effectiveness between the ordinary quantile regression and ER simultaneously. Motivated by a longitudinal ACTG 193A data with nonignorable dropouts, we propose a two-stage estimation procedure and statistical inference methods based on the kth power ER and empirical likelihood to accommodate both the within-subject correlations and nonignorable dropouts. Firstly, we construct the bias-corrected generalized estimating equations by combining the kth power ER and inverse probability weighting approaches. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Secondly, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function to obtain the improved empirical likelihood procedures. The asymptotic properties of the corresponding estimators and their confidence regions are derived. The finite-sample performance of the proposed estimators is studied through simulation and an application to the ACTG 193A data is also presented.

第k个 ($1<ķ\le 2$) 幂期望回归 (ER) 可以同时平衡普通分位数回归和 ER 之间的稳健性和有效性。受具有不可忽略辍学的纵向 ACTG 193A 数据的启发，我们提出了一种基于k次方 ER 和经验可能性的两阶段估计程序和统计推断方法，以适应受试者内相关性和不可忽略的辍学。首先，我们通过组合k来构造偏差校正的广义估计方程次幂 ER 和逆概率​​加权方法。随后，基于充分的工具估计方程，利用广义矩方法估计不可忽略的辍学倾向中的参数。其次，为了在一个信息丰富的工作相关结构下合并被试内的相关性，我们借用二次推理函数的思想来获得改进的经验似然程序。推导出相应估计量及其置信区域的渐近性质。通过仿真研究了所提出的估计器的有限样本性能，并介绍了对 ACTG 193A 数据的应用。