Various non-parametric goodness of fit tests have already been investigated in the literature. However, those tests are rarely used in the case of missing observations. We here study the goodness of fit test for missing data based on L_p distances along with Kolmogorov–Smirnov and Cramer–von-Mises distances when missingness occurs at random. The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives that enable us to investigate the asymptotic local power of the tests. We also study the performance of the tests for finite samples using simulation, and the tests perform well for those cases. The usefulness of the tests is illustrated on three real data sets.

中文翻译：

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关于随机发生缺失时缺失数据的基于距离的拟合优度检验

文献中已经研究了各种非参数拟合优度检验。但是，这些测试很少用于缺少观察的情况。我们在这里研究了基于L _p距离以及 Kolmogorov-Smirnov 和 Cramer-von-Mises 距离的缺失数据拟合优度，当缺失随机发生时。所提出的检验统计量的渐近分布是在连续的替代方案下得出的，这使我们能够研究检验的渐近局部功效。我们还使用模拟研究了有限样本测试的性能，这些测试在这些情况下表现良好。在三个真实数据集上说明了测试的有用性。