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.
Citation
A. P. Korostelev. L. Simar. A. B. Tsybakov. "Efficient Estimation of Monotone Boundaries." Ann. Statist. 23 (2) 476 - 489, April, 1995. https://doi.org/10.1214/aos/1176324531
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