## The Annals of Statistics

### Efficient Estimation of Monotone Boundaries

#### 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

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