Group for Research in Decision Analysis

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.