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.
Publié le : 1995-04-14
Classification:
Monotone boundary,
free disposal hull,
Hausdorff distance,
efficiency,
minimum risk,
estimation of support of a density,
62G05,
62G20
@article{1176324531,
author = {Korostelev, A. P. and Simar, L. and Tsybakov, A. B.},
title = {Efficient Estimation of Monotone Boundaries},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 476-489},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324531}
}
Korostelev, A. P.; Simar, L.; Tsybakov, A. B. Efficient Estimation of Monotone Boundaries. Ann. Statist., Tome 23 (1995) no. 6, pp. 476-489. http://gdmltest.u-ga.fr/item/1176324531/