Independence tests for randomly censored data: novel proposal and the review of recent developments

Abstract

Here we consider the problem of testing independence between two random variables in the presence of random censoring. In particular, we consider three different censoring scenarios: one of the targeted variables is censored, both targeted variables are censored with the same censoring variable and both targeted variables are censored with different censoring variables. In all three cases, some well-known, as well as novel adaptations of several famous test statistics for testing independence (designed for complete data) are presented. Their limiting null distributions are shown, accompanied by the proposal of resampling procedures that might be used for their approximation. Finally, the results of wide empirical power are summarized and directions for further research are presented.