This article shows that, when variables with missing values are linearly related to observed variables, the normal-distribution-based pseudo MLEs are still consistent. The population distribution may be unknown while the missing data process can follow an arbitrary missing at random mechanism. Enough details are provided for the bivariate case so that readers having taken a course in statistics/probability can fully understand the development. Sufficient conditions for the consistency of the MLEs in higher dimensions are also stated, while the details are omitted.

中文翻译：

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当数据随机丢失时，基于正态分布的伪最大似然估计的一致性

本文表明，当有缺失值的变量与观察变量线性相关时，基于正态分布的伪 MLE 仍然是一致的。人口分布可能是未知的，而缺失数据过程可以遵循任意随机缺失机制。为二元案例提供了足够的详细信息，以便参加过统计/概率课程的读者可以充分了解发展。还说明了在更高维度上 MLE 一致性的充分条件，而省略了细节。