Random rates in anisotropic regression
Random rates in anisotropic regression
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DOI：
10.1214/aos/1021379858
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发表时间：
2002-04-01
影响因子：
4.5
通讯作者：
Lepski, O
中科院分区：
文献类型：
--
作者：
Hoffmann, M;Lepski, O
在极大极小理论的背景下，我们提出了一种新的风险，标准化的随机变量，可测量的数据。我们提出了一个最优性的概念和方法来构建相应的最优程序。我们应用这个一般设置的问题，选择显着的变量在高斯白色噪声。特别是，我们表明，我们的方法从根本上提高了估计的准确性，在这个意义上给予明确的改进的L-2-范数的置信集。自适应估计的链接进行了讨论。
In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in L-2-norm. Links to adaptive estimation are discussed.