Hanna Jankowski

York University

Title: Nonparametric
Estimation of a Hazard Function under Shape Constraints.

Abstract: In a large population, it is often natural to assume that the hazard function is U-shaped, or bathtub shaped. The nonparametric maximum likelihood estimator in this situation was first considered by Grenander in 1956, and has been shown to converge at rate $n^{1/3}$. Making the additional assumption that the hazard function is also convex, increases the convergence rate to $n^{2/5}$. The goal of this talk is to explain why the $n^{1/3}$ and $n^{2/5}$ rates are achieved.