title: ON THE GRENANDER ESTIMATOR AT ZERO.
abstract: We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the situation when the true density f(0) is unbounded at zero, with different rates of growth to infinity. In the course of our study we develop new switching relations using tools from convex analysis. The theory is applied to a problem involving mixtures.
authors.affiliation: Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Paris, 75775, France.
authors.forename: Fadoua
authors.initials: F
authors.lastname: Balabdaoui
authors.forename: Hanna
authors.initials: H
authors.lastname: Jankowski
authors.forename: Marios
authors.initials: M
authors.lastname: Pavlides
authors.forename: Arseni
authors.initials: A
authors.lastname: Seregin
authors.forename: Jon
authors.initials: J
authors.lastname: Wellner