This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some covariates. The target is a marginal location parameter given through an M-functional. To obtain robust Fisher-consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values assuming a missing at random condition. Three methods are considered to estimate the marginal distribution which allows to obtain the M-location of interest: the well-known inverse probability weighting, a convolution-based method that makes use of the regression model and an augmented inverse probability weighting procedure that prevents against misspecification. Different aspects of their asymptotic behaviour are derived under regularity conditions. The robust studied estimators and their classical relatives are compared through numerical experiments under different missing data models, including clean and contaminated samples. The methodology is illustrated through a real data set.

中文翻译：

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随机缺失协变量和响应的回归模型中的稳健位置估计器

当响应和某些协变量中出现缺失数据时，本文讨论了通用回归模型下的稳健边际估计。目标是通过 M 函数给出的边缘位置参数。为了获得稳健的 Fisher 一致估计量，需要考虑适当定义的边际分布函数估计量。这些估计器避免了由于假设随机条件缺失而导致的缺失值的偏差。考虑了三种方法来估计允许获得感兴趣的 M 位置的边际分布：众所周知的逆概率加权，一种利用回归模型的基于卷积的方法和一个增强的逆概率加权过程，以防止错误说明。它们的渐近行为的不同方面是在规律性条件下导出的。通过数值实验在不同的缺失数据模型（包括干净和受污染的样本）下比较稳健研究的估计量及其经典相关估计量。该方法通过一个真实的数据集来说明。