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Article Dans Une Revue Annales de l'ISUP Année : 1995

On Estimation Of Monotone And Convex Boundaries

Résumé

We study the problem of estimating a set G in IR (or, equivalently, estimating its boundary) given n independent identically distributed in G observations X^,...,X. We suppose that the boundary of G can be represented as a monotone or convex function of k-1 arguments. We evaluate the risks of several estimators of boundaries and show that they converge with the best possible rates. A general density of X.'s with the support G is considered, as well as the extension to the case where a small portion of "data outliers" falls out of the set G.
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hal-03659948 , version 1 (05-05-2022)

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  • HAL Id : hal-03659948 , version 1

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A Korostelev, L Simar, A Tsybakov. On Estimation Of Monotone And Convex Boundaries. Annales de l'ISUP, 1995, XXXIX (1), pp.3-18. ⟨hal-03659948⟩
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