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
More Info
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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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