In this paper, we study the weighted quantile average estimation technique for the parameter in additive partially linear models with missing covariates, which is proved to be an efficient method. The proposed method is based on optimally combining information over different quantiles via multiple quantile regression. We establish asymptotic normality of the weighted quantile average estimators when the selection probability is known, estimated using the non-parametrical method and parametrical method, respectively. Moreover, we compute optimal weights by minimizing asymptotic variance and then obtain the corresponding optimal weighted quantile average estimators. To examine the finite performance of our proposed method, we use the numerical simulations and apply to model time sober for the patients from a rehabilitation center. Simulation results and data analysis further verify that the proposed method is an efficient and safe alternative to both the WCQR method and WLS method.

中文翻译：

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协变量缺失的加法部分线性模型中参数的有效估计

在本文中，我们研究了缺少协变量的加法部分线性模型中参数的加权分位数平均估计技术，这被证明是一种有效的方法。所提出的方法基于通过多分位数回归将不同分位数上的信息进行最佳组合。我们建立时选择概率是已知的，使用非参数的方法和参数化方法，分别估计的加权平均位数估计的渐近正态性。此外，我们通过最小化渐近方差来计算最佳权重，然后获得相应的最佳加权分位数平均估计量。为了检验我们提出的方法的有限性能，我们使用了数值模拟，并将其应用于康复中心患者的清醒时间建模。