On the Grenander estimator at zero

2009/02/25 by Fadoua Balabdaoui, Balabdaoui, Fadoua, Hanna Jankowski +8
Mathematics · #62G05 #62G07 #62G20 #62G32 #FOS: Mathematics #Functional Equations Stability Results #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G07 #msc:62G20 #msc:62G32 #stat.TH

paper · pdf · doi:10.48550/arxiv.0902.4453

28 pages. See also: http://www.stat.washington.edu/www/research/reports/2009/tr554r1 http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.html

openalex publication_date 2009/02/25 · arxiv created 2009/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 f₀ is unbounded at zero, with different rates of growth to infinity. In the course of our study we develop new switching relations by use of tools from convex analysis. The theory is applied to a problem involving mixtures.

Citations

• The statistical theory of the strength of bundles of threads. I

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