Nonparametric inference under dependent truncation

Data truncation is a problem in scientific investigations. So far, statistical models and inferences are mostly based on the assumption that the survival and truncation times are independent, which can be unrealistic in applications. In a nonparametric setting, we discuss identifiability of the conditional and unconditional survival and hazard functions when the survival times are subject to dependent truncation, namely, the survival time is dependent on the truncation time. Nonparametric kernel estimators of these unknowns are proposed. Usefulness of the nonparametric estimators is demonstrated through their theoretical properties, an application and a simulation study.