Nonparametric Curve Estimation for Truncated and Censored Data Without Product-Limit

Analysis of truncated and censored data is a familiar part of actuarial practice, and so far the product-limit methodology, with Kaplan-Meier estimator being its vanguard, has been the main statistical tool. At the same time, for the case of directly observed data, the sample mean methodology yields both efficient estimation and dramatically simpler statistical inference. This paper shows that for truncated and censored data a sample mean approach is natural in estimation of the hazard rate (also called the force of mortality and failure rate), and note that in actuarial science this characteristic of a random variable is often of interest on its own. Further, the proposed sample mean approach allows us to understand what and why we can and cannot estimate for truncated and censored data. In particular, it is explained why in general only a conditional density can be estimated. Results are illustrated via simulated and real examples.