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Abstract:
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Estimation of the convex support of a density is already well understood, if direct observations from that density are available. In general, very natural estimators, such as the convex hull of the sample, turn out to be optimal in a minimax sense. In this talk, we investigate the following inverse problem: How can one estimate the support of a density, when it is known to be convex, but when the observations are contaminated by some additive noise ?
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