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.

翻译：本文提出了Aleksi\'c (2024) 所开发的基于U统计量的MCAR检验的一个推广版本。与原始检验类似，该新检验通过计算并组合响应指标与数据变量之间的协方差来检验MCAR假设。然而，与旧检验不同，它能够利用部分观测变量，从而显著扩大了可检测备择假设的范围。新检验似乎校准良好，远优于用作基准的Little MCAR检验。对于旧检验可检测的备择假设，新检验的功效与旧检验相当（尽管略低），但在所有研究场景中仍能优于Little检验。对于先前无法检测或几乎无法检测的备择假设，新检验在三种方法中表现最佳。新检验具有与Little检验相同的数据四阶矩有限的假设。结果表明，新检验对该假设更具稳健性，尽管两种检验具有相似的局限性。