The limit distribution of the L∞-error of Grenander-type estimators
Journal Article
(2012)
Author(s)
C Durot (External organisation)
VN Kulikov (External organisation)
Hendrik P. Lopuhaa (TU Delft - Statistics)
Research Group
Statistics
DOI related publication
https://doi.org/10.1214/12-AOS1015SUPP
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https://resolver.tudelft.nl/uuid:77b9a516-db9f-4993-a4d2-38598b251be8
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Publication Year
2012
Language
English
Research Group
Statistics
Issue number
3
Volume number
40
Pages (from-to)
1578-1608
Abstract
Let ƒ be a nonincreasing function defined on [0,1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between ƒ and its Grenander-type estimator on sub-intervals of [0,1]. The rate of convergence is found to be of order (n/log n)−1/3 and the limiting distribution to be Gumbel.
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