Jackknife methods for left-truncated data

Let U * and V * be two independent positive random variables with continuous distribution functions F and G, respectively. Under random truncation, both U * and V * are observable only when U * ≥ V * . Let F ¯ n be the nonparametric maximum likelihood estimate (Lynden-Bell, 1971) of F ¯ = 1 − F . In this paper, it is shown that the jackknife variance estimate of F ¯ n consistently estimates the limit variance. In a simulation study, we show that the jackknife works satisfactorily for moderate sample size. As an illustration we also apply our method to a real set of AIDS data.