A law of the iterated logarithm for Grenander's estimator

Lutz Duembgen, Jon A. Wellner, Malcolm Wolff

In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0)>0$, $f^{\prime }(t_0)<0$, and $f^{\prime }$ is continuo…