This paper considers statistical inference for partially linear models Y = X(T)mu + nu(Z) + epsilon when the linear covariate X is missing with missing probability pi depending upon (Y, Z). We propose empirical likelihood based statistics to construct confidence regions for beta and nu(z). The resulting statistics are shown to be asymptotically chi-squared distributed. Finite sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a data set from an AIDS clinical trial.

中文翻译：

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缺少协变量的部分线性模型的基于经验似然的推理

本文考虑了部分线性模型 Y = X(T)mu + nu(Z) + epsilon 的统计推断，当线性协变量 X 缺失时，缺失概率 pi 取决于 (Y, Z)。我们提出了基于经验似然的统计数据来构建 beta 和 nu(z) 的置信区域。结果统计数据显示为渐近卡方分布。所提出的统计数据的有限样本性能通过模拟实验进行评估。所提出的方法应用于来自艾滋病临床试验的数据集。