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Efficient estimation of monotone boundaries. (English) Zbl 0829.62043

Summary: Let \(g : [0,1] \to [0,1]\) be a monotone nondecreasing function and let \(G\) be the closure of the set \(\{(x,y) \in [0,1] \times [0,1]\): \(0 \leq y \leq g(x)\}\). 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.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62C20 Minimax procedures in statistical decision theory
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