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.


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