Title: On hazard rate estimation for censored data
Authors: Mathieu Sart - Univ Lyon, UJM-Saint-Etienne, Institut Camille Jordan (France) [presenting]
Abstract: The hazard rate is proposed to be estimated from censored data by broadening a recent estimation method based on models and named rho-estimation. As we shall see, this method may reduce to the one of maximum likelihood under suitable assumptions. However, the two methods differ in general. In particular, rho-estimation also applies to numerous models where the maximum likelihood method does not work. Besides, rho-estimators generally possess better robustness properties. As a hazard rate cannot be uniformly estimated on the positive real line, we propose to evaluate the quality of the estimators by means of a random Hellinger-type loss adapted to the statistical setting. We establish non-asymptotic risk bounds that are very similar to the ones that can be obtained in density estimation. We then specify these bounds under some assumptions on the hazard rate.