文章基本信息

标题：On polyhedral estimation of signals via indirect observations
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作者：Anatoli Juditsky ; Arkadi Nemirovski
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：1
页码：458-502
DOI：10.1214/19-EJS1661
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Functional estimation; statistical linear inverse problems; nonlinear estimation; sketching