Bootstrap Methods for Truncated and Censored Data

For right censored data, Efron (1981) has shown that his “simple” and “obvious” methods of bootstrapping are equivalent. We explain why this equivalence no longer holds for truncated data. Wang (1991) generalized Efron’s “obvious” bootstrap method to data that are both left truncated and right censored, under the assumption that C ≥ T and C − T is independent of T , where T and C denote the (generic) censoring and truncation variables. We discuss how the “obvious” bootstrap method can be extended when this independence assumption is removed, and also develop an asymptotic theory of the “simple” bootstrap method for left truncated and right censored data, showing that the “simple” bootstrap approximations to the sampling distributions of various nonparametric statistics from these data are accurate to the order of Op(n −1).