Adaptive Estimation of Hazard Rate with Censored Data

Abstract

In this article, we study hazard projection estimators under right-censoring of the observations. We consider projection spaces generated by trigonometric or piecewise polynomials. First, we derive bounds on the MISE of the estimators. These bounds imply that the estimator reaches the standard optimal rate associated with the regularity of the hazard function, provided that the dimension of the projection space is relevantly chosen. Then we provide an adaptive procedure leading to an automatic choice of this dimension via a penalized minimum contrast estimator. Our procedure is based on a data-driven random penalty function. The resulting estimator automatically reaches the optimal rate.

Keywords:

• Adaptive estimation
• Hazard rate
• Minimax rate
• Nonparametric penalized contrast estimator

Mathematics Subject Classification:

• 62G05
• 62G20