Detection of correlations
Detection of correlations
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DOI：
10.1214/11-aos964
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发表时间：
2011-06
影响因子：
4.5
通讯作者：
E. Arias-Castro;Sébastien Bubeck;G. Lugosi
中科院分区：
文献类型：
--
作者：
E. Arias-Castro;Sébastien Bubeck;G. Lugosi
我们考虑的假设检验问题，决定是否观察到的高维向量有独立的正常成分，或者，如果它有一个小的相关组件的子集。相关分量可以具有统计学家已知的某种组合结构。我们建立的最坏情况下（极大极小）的风险的相关子集的大小，相关性的水平，和结构的类可能相关的集的上限和下限。我们发现，一些简单的测试在许多情况下具有接近最优的性能，而广义似然比测试是次优的，在一些重要的情况下。
We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of possibly correlated sets. We show that some simple tests have near-optimal performance in many cases, while the generalized likelihood ratio test is suboptimal in some important cases.