Groupe d’études et de recherche en analyse des décisions

# On the Grenander estimator at zero

## Hanna Jankowski

The Grenander estimator is the maximum likelihood estimator of a decreasing density defined on the positive real line under IID sampling. Assuming that the true density $$f$$ is continuous, then the estimator is uniformly consistent on sets bounded away from zero. However, the estimator diverges at the point $$x=0$$, even if the true density is bounded everywhere. In this talk, I will discuss some recent results on the behaviour of the Grenander estimator near zero under a variety of hypotheses on the growth of $$f$$ near zero.