In this paper, with an assumed parametric model for the selection probability function, a robust model averaging estimation method is proposed for partially linear models with responses missing at random. The method is based on a weighted Mallows-type criterion. The method is robust in the sense that the asymptotic optimality holds true as long as the true model of the selection probability function is some measurable function of its assumed model. The optimal weight vector for model averaging is obtained by minimizing the weighted Mallows-type criterion. It is shown that the robust model averaging method achieves the lowest possible squared error asymptotically. Some simulation studies were conducted to evaluate the proposed method. An application to two real examples are provided as illustration.

中文翻译：

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针对随机丢失响应的部分线性模型的稳健模型平均方法

本文利用选择概率函数的假设参数模型，针对响应随机丢失的部分线性模型提出了一种稳健的模型平均估计方法。该方法基于加权 Mallows 型标准。该方法是稳健的，因为只要选择概率函数的真实模型是其假设模型的某个可测量函数，渐近最优性就成立。通过最小化加权 Mallows 型准则来获得模型平均的最佳权重向量。结果表明，鲁棒模型平均方法渐近地实现了尽可能最低的平方误差。进行了一些模拟研究来评估所提出的方法。提供了两个实际示例的应用作为说明。