
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 publiéDate
2011Journal name
Statistica SinicaVolume
21Number
2Publisher
Institute of Statistical Science
Pages
873-900
Metadata
Show full item recordAbstract (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 relationsRelated items
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