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Optimal rates of convergence for convex set estimation from support functions. (English) Zbl 1246.62085

Summary: We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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References:

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