Minimax Rates for Statistical Inverse Problems Under General Source Conditions

被引：7

作者：

Ding, Litao ^{[1
]}

Mathe, Peter ^{[2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Weierstrass Inst, Mohrenstr 39, D-10117 Berlin, Germany

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2018年 / 18卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Statistical Inverse Problem; General Source Condition; Minimax Rate; ILL-POSED PROBLEMS; HILBERT SCALES; REGULARIZATION;

D O I：

10.1515/cmam-2017-0055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to the seminal study by D. L. Donoho, R. C. Liu, and B. MacGibbon [4]. These authors highlighted the special role of the truncated series estimator, and for such estimators the risk can explicitly be given. We provide several examples, indicating results for statistical estimation in ill-posed problems in Hilbert space.

引用

页码：603 / 608

页数：6

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