To impute or to adapt? Model specification tests' perspective

We study the problem of testing a wide range of statistical hypotheses under the assumption of the sample being randomly right-censored. As an alternative to the classical approach which assumes the modification of a test statistic for complete data, we propose a novel imputation procedure. The new approach, for the first time, is completely hypothesis free which means that it does not require any modification for the application of different statistical procedures. The competitive properties are demonstrated with several goodness-of-fit tests to exponentiality, as well as the most well known two-sample tests. Finally, concluding remarks about whether it is better to impute data or to adapt statistical procedures are provided.