标题： 基于U统计量的MCAR检验的推广：利用部分观测变量 显示英文标题

标题： A generalization of a U-statistics-based MCAR Test: Utilizing Partially Observed Variables

摘要： 在本文中，提出了一种由Aleksić（2024）开发的基于U统计量的MCAR检验的广义版本。 该新检验与原始检验类似，通过计算和结合响应指示变量与数据变量之间的协方差来检验MCAR。 然而，与旧检验不同的是，它能够利用部分观测变量，从而导致可检测替代假设的类别显著增大。 该新检验似乎校准得非常好，比用作基准的Little的MCAR检验要好得多。 对于旧检验可以检测的替代假设，新检验的效力与旧检验相当，尽管稍低一些，但在所有研究的场景中仍能优于Little的检验。 对于之前无法检测或 barely 检测的替代假设，新检验是三者中表现最好的。 新检验与旧检验具有相同的假设，即数据的有限四阶矩，这是Little检验所需的相同假设。 结果表明，新检验对该假设更具鲁棒性，尽管两种检验都有类似的局限性。 显示英文摘要

摘要： In this paper, a generalized version of a U-statistics-based test for MCAR developed by Aleksi\'c (2024) is presented. The novel test, similar to the original, tests for MCAR by calculating and combining the covariances between the response indicators and the data variables. However, unlike the old test, it is able to utilize partially observed variables, resulting in a significantly larger class of detectable alternatives. The novel test appears to be well calibrated, much better than the Little's MCAR test that was used as a benchmark. For the alternatives that were detectable for the old test, the novel test has comparable, although slightly lower, power as the old one, but is still able to outperform Little's test in all of the studied scenarios. For alternatives that were previously undetectable or barely detectable, the novel test performs the best of three. The novel test has the same assumption of finite fourth moments of the data, the same assumption necessary for Little's test. The results indicate that the novel test is more robust to this assumption, although both tests have similar limitations.