On distance based goodness of fit tests for missing data when missing occurs at random

Summary 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 Lp 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. Non‐parametric goodness of fit tests which are based on Lp distances including the well known Kolmogorov‐Smirnov and Cramer‐von‐Mises distances are studied under missing data when the missing mechanism is random (MAR). The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives. Then we also investigate the asymptotic local power of the tests.