The limit distribution of the L∞-error of Grenander-type estimators

Journal article (2012)

Authors

Cécile Durot External organisation
VN Kulikov External organisation
H.P. Lopuhaä Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
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Published Date

2012

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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.