文章基本信息

标题：Solution of linear ill-posed problems by model selection and aggregation
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作者：Felix Abramovich ; Daniela De Canditiis ; Marianna Pensky 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：1
页码：1822-1841
DOI：10.1214/18-EJS1447
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection estimator selects a single model by minimizing the penalized empirical risk over all possible models. By contrast with direct problems, the penalty depends on the model itself rather than on its size only as for complexity penalties. A Q-aggregate estimator averages over the entire collection of estimators with properly chosen weights. Under mild conditions on the dictionary, we establish oracle inequalities both with high probability and in expectation for the two estimators. Moreover, for the latter estimator these inequalities are sharp. The proposed procedures are implemented numerically and their performance is assessed by a simulation study.