Doubly protected methods are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector \(\mathbf {X}\) of covariates is observed at each individual, and the missing mechanism is assumed to be independent of the response, conditioned on \(\mathbf {X}\) (missing at random). In recent years, many authors have turned from the estimation of the mean to that of the median, and more generally, doubly protected estimators of the quantiles have been proposed. In this work, we present doubly protected estimators for the quantiles in semiparametric models that are also robust, in the sense that they are resistant to the presence of outliers in the sample.

中文翻译：

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缺少数据的分位数的鲁棒双重保护估计

双重保护方法广泛用于从样本中某些人缺少响应的样本中估计结果Y的总体平均值。为了补偿缺失的响应，在每个个体上观察到协变量的向量\（\ mathbf {X} \），并且假定缺失机制与响应无关，其条件是\（\ mathbf {X} \）（随机丢失）。近年来，许多作者已经从均值的估计转向中值的估计，并且更普遍地，提出了对分位数进行双重保护的估计器。在这项工作中，我们提出了半参数模型中分位数的双重保护估计量，该估计量也很健壮，因为它们可以抵抗样本中离群值的存在。