Nonparametric estimation of a delay distribution based on left-censored and right-truncated data

This paper proposes a nonparametric method for estimating a delay distribut ion based on left-censored and right-truncated data. A variance-covariance estimator is provided. The method is applied to the Australian AIDS data in which some data are left censored and some data are not left censored. Thi s situation arises with AIDS case-reporting data in Australia because repor ting delays were recorded only from November 1990 rather than from the begi nning of the epidemic there. It is shown that inclusion of the left-censore d data, as opposed to analyzing only the uncensored data, improves the prec ision of the estimate.