Statistical Estimation and Optimal Recovery
Statistical Estimation and Optimal Recovery
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DOI：
10.1214/aos/1176325367
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发表时间：
1994-03
影响因子：
4.5
通讯作者：
D. Donoho
中科院分区：
文献类型：
--
作者：
D. Donoho
本文给出了由受随机高斯噪声污染的间接数据估计未知对象的线性泛函的极小极大线性风险的新公式。该公式覆盖了各种损失函数，并且不需要凸先验类的对称性。结果表明，仿射极大极小规则是极小极大的几个百分点内，甚至在非线性规则，各种损失函数。它还表明，估计的难度是衡量的模的连续性的功能估计。证明方法揭示了统计估计问题中的极大极小仿射估计与最优恢复理论中的最优算法之间的对应关系。
New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions, and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of loss functions. It is also shown that difficulty of estimation is measured by the modulus of continuity of the functional to be estimated. The method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery.