Korostelev, AP.
Simar, Léopold
[UCL]
Tsybakov, AB.
Let g: [0,1] --> [0,1] be a monotone nondecreasing function and let G be the closure of the set {(x, y) is an element of [0,1] X [0,1]: 0 less than or equal to y less than or equal to 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.
Bibliographic reference |
Korostelev, AP. ; Simar, Léopold ; Tsybakov, AB.. Efficient Estimation of Monotone Boundaries. In: Annals of Statistics, Vol. 23, no. 2, p. 476-489 (1995) |
Permanent URL |
http://hdl.handle.net/2078.1/47953 |