A single-index regression model is considered, where some responses in the model are assumed to be missing at random. Local linear rank-based estimators of the single-index direction and the unknown link function are proposed. Asymptotic properties of the estimators are established under mild regularity conditions. Monte Carlo simulation experiments show that the proposed estimators are more efficient than their least squares counterparts especially when the data are derived from contaminated or heavy-tailed model error distributions. When the errors follow a normal distribution, the least squares index direction estimator tends to be more efficient than the rank-based index direction estimator; however, the least squares link function estimator remains less efficient than the rank-based link function estimator. A real data example is analyzed and cross-validation studies show that the proposed procedure provides better prediction than the least squares method when the responses contain outliers and are missing at random.

中文翻译：

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随机缺失响应的单指标模型的稳健估计

考虑了单指数回归模型，其中假设模型中的某些响应随机丢失。提出了单索引方向和未知链接函数的基于局部线性秩的估计器。估计量的渐近性质是在温和的规律性条件下建立的。蒙特卡罗模拟实验表明，所提出的估计量比最小二乘法更有效，尤其是当数据来自污染或重尾模型误差分布时。当误差服从正态分布时，最小二乘索引方向估计器往往比基于秩的索引方向估计器更有效；然而，最小二乘链接函数估计器的效率仍然低于基于秩的链接函数估计器。