Open Access
April, 1995 Efficient Estimation of Monotone Boundaries
A. P. Korostelev, L. Simar, A. B. Tsybakov
Ann. Statist. 23(2): 476-489 (April, 1995). DOI: 10.1214/aos/1176324531


Let $g: \lbrack 0, 1\rbrack \rightarrow \lbrack 0, 1\rbrack$ be a monotone nondecreasing function and let $G$ be the closure of the set $\{(x, y) \in \lbrack 0, 1\rbrack \times \lbrack 0, 1\rbrack: 0 \leq y \leq g (x)\}$. We consider the problem of estimating the set $G$ from a sample of i.i.d. observations uniformly distributed in $G$. The estimation error is measured in the Hausdorff metric. We propose the estimator which is asymptotically efficient in the minimax sense.


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A. P. Korostelev. L. Simar. A. B. Tsybakov. "Efficient Estimation of Monotone Boundaries." Ann. Statist. 23 (2) 476 - 489, April, 1995.


Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0829.62043
MathSciNet: MR1332577
Digital Object Identifier: 10.1214/aos/1176324531

Primary: 62G05
Secondary: 62G20

Keywords: efficiency , estimation of support of a density , free disposal hull , Hausdorff distance , minimum risk , Monotone boundary

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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