Nonparametric Hazard Rate Estimation for Current Status Censoring

Hazard rate, also known as the force of mortality and failure rate, defines the instantaneous rate of an event occurring at a specific point in time, given that the event has not occurred up to that point. Hazard rate is one of the main characteristics of random variables studied in the survival analysis with wide applications in medicine, finance, insurance and engineering to predict failures, outcomes, and risks. Under current status censoring the event of interest is never observed, instead at a random monitoring time status of the event is given, namely it is known that the event either already occurred or not. For this setting and under the mean integrated squared error criterion, lower and upper bounds for nonparametric hazard rate estimation are presented, and methodology of data-driven estimation is proposed and tested.