Estimation of the density for censored and contaminated data

Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age.