| Nonparametric estimation of the hazard rate function, based on data modified by left truncation and/or right censoring, is considered. The hazard rate is not integrable over its support and hence it is traditionally estimated over a fixed interval under the mean integrated squared error (MISE) criterion. It is well known in the literature that neither left truncation nor right censoring affect the rate of the MISE convergence, but so far no results on how the modified data and the interval of estimation affect the MISE convergence have been known. To understand the affect, asymptotic theory of sharp minimax estimation is developed which indicates how the modified data and the interval of estimation affect the MISE convergence. The theory is complemented by presenting a data-driven estimator for small samples which is tested on numerical simulations and real data. |
