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On the Grenander Estimator at Zero

Balabdaoui, Fadoua; Jankowski, Hanna; Pavlides, Marios; Seregin, Arseni; Wellner, Jon (2011), On the Grenander Estimator at Zero, Statistica Sinica, 21, 2, p. 873-900

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Statistica Sinica
Volume
21
Number
2
Publisher
Institute of Statistical Science
Pages
873-900
Metadata
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Author(s)
Balabdaoui, Fadoua
Jankowski, Hanna
Pavlides, Marios
Seregin, Arseni
Wellner, Jon
Abstract (EN)
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.
Subjects / Keywords
Convex analysis; inconsistency; limit distribution; maximum likelihood; mixture distributions; monotone density; nonparametric estimation; Poisson process; rate of growth; switching relations