We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

中文翻译：

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随机缺失数据的响应均值的平均经验似然推断

我们将响应均值的平均经验似然推断扩展为随机丢失的数据。当随机丢失响应时，尤其是当协变量是高维且样本量​​较小时，经验似然比置信区域很差。因此，我们开发了三种偏差校正的均值经验似然方法，以获得对响应均值的有效推断。对于三个经过偏差校正的估计方程，我们通过生成成对均值数据集获得了一个新集合。该方法可以增加用于估计的样本的大小，并减少尺寸诅咒的影响。建立了最大平均经验似然估计量的一致性和渐近正态性。通过仿真给出了所提出估计量的有限样本性能，