Adaptive nonparametric confidence sets
Adaptive nonparametric confidence sets
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DOI：
10.1214/009053605000000877
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发表时间：
2006-02-01
影响因子：
4.5
通讯作者：
Van der Vaart, Aad
中科院分区：
文献类型：
--
作者：
Robins, James;Van der Vaart, Aad
我们在各种统计模型中为Hilbert空间值参数构造诚实的置信区域。置信集可以以任意自适应估计为中心，并且具有最佳适应于给定模型选择的直径。后一种调整必然在范围上受到限制。我们回顾了自适应置信区域的概念，并将自适应置信区域的直径的最佳比率与用于测试和估计的最小最大比率相关联。应用包括有限正态均值模型、白色噪声模型、密度估计和随机设计回归。
We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.