The Annals of Statistics

Efficient Estimation of Monotone Boundaries

A. P. Korostelev, L. Simar, and A. B. Tsybakov

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 23, Number 2 (1995), 476-489.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324531

Digital Object Identifier
doi:10.1214/aos/1176324531

Mathematical Reviews number (MathSciNet)
MR1332577

Zentralblatt MATH identifier
0829.62043

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

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

Citation

Korostelev, A. P.; Simar, L.; Tsybakov, A. B. Efficient Estimation of Monotone Boundaries. Ann. Statist. 23 (1995), no. 2, 476--489. doi:10.1214/aos/1176324531. https://projecteuclid.org/euclid.aos/1176324531


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