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# Title: On Polyhedral Estimation of Signals via Indirect Observations

Abstract: We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear in observations "polyhedral" estimate along with computation-friendly techniques for its design and risk analysis. We demonstrate that under favorable circumstances the resulting estimate is provably near-optimal in the minimax sense, the "favorable circumstances" being less restrictive than the weakest known so far assumptions ensuring near-optimality of estimates which are linear in observations.
 Subjects: Statistics Theory (math.ST) MSC classes: 62G05, 62H12, 62C20 Cite as: arXiv:1803.06446 [math.ST] (or arXiv:1803.06446v1 [math.ST] for this version)