Non-Parametric Hazard Rate Estimation under Progressive Type-II Censoring

Publisher In survival-analysis studies, estimators of the slope of cumulative-hazard-rate function provide only a crude estimate for the hazard-rate function. For this reason, it is important to estimate directly the hazard-rate function, which is the quantity of interest in many practical applications. This chapter describes how the Ramlau–Hansen-type estimator may be used to estimate the hazard-rate function based on progressively Type II censored data. This scheme of censoring has been suggested in life-testing experiments. Units may be removed at various stages during the experiment, resulting from the experiment itself or to reduce its cost and/or its duration. The Nelson–Aalen-type estimator of the cumulative-hazard-rate function and the corresponding kernel estimator are mentioned along with the properties of this estimator by using the results of Andersen et al. The practical choice of an optimal bandwidth and the results of a simulation study are also presented.