Le 5 novembre 2010, 15:30, CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214.
On the Grenander estimator at zero
Hanna Jankowski, York University
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.