A conditional bootstrap procedure for reconstruction of the incubation period of AIDS

Data on the incubation period of AIDS patients are often fragmented and censored. parametric models have been proposed in the literature to impute the missing segment of the incubation period. The numerical results vary widely with the parametric models used. We propose a nonparametric conditional bootstrap (CB) procedure for imputation. The quality of the CB data is studied by checking the asymptotic accuracy of the CB estimators. We establish the asymptotic accuracy of the CB procedure for two basic nonparametric estimators: the empirical distribution function and a kernel-type conditional empirical distribution function. The rates of convergence of the CB approximation are obtained. The results for the kernel-type estimators hold also for the nearest-neighbor-type estimators.