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2020 On polyhedral estimation of signals via indirect observations
Anatoli Juditsky, Arkadi Nemirovski
Electron. J. Statist. 14(1): 458-502 (2020). DOI: 10.1214/19-EJS1661


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.


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Anatoli Juditsky. Arkadi Nemirovski. "On polyhedral estimation of signals via indirect observations." Electron. J. Statist. 14 (1) 458 - 502, 2020.


Received: 1 April 2019; Published: 2020
First available in Project Euclid: 24 January 2020

zbMATH: 07163264
MathSciNet: MR4055097
Digital Object Identifier: 10.1214/19-EJS1661

Primary: 62H12 , 62J05
Secondary: 62G08

Keywords: Functional estimation , nonlinear estimation , sketching , statistical linear inverse problems


Vol.14 • No. 1 • 2020
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