Detecting Positive Correlations in a Multivariate Sample
Detecting Positive Correlations in a Multivariate Sample
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DOI：
10.3150/13-bej565
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发表时间：
2012-02
期刊：
影响因子：
1.5
通讯作者：
E. Arias-Castro;Sébastien Bubeck;G. Lugosi
中科院分区：
文献类型：
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作者：
E. Arias-Castro;Sébastien Bubeck;G. Lugosi
本文研究多元正态总体的相关矩阵是否为单位矩阵的检验问题。我们专注于稀疏类的替代品，只有少数条目是非零的，事实上，积极的。我们推导出一个一般的下界适用于各种类和研究的性能，一些接近最优的测试。我们特别关注计算可行性并构建可以有效计算的接近最佳的测试。最后，我们应用这些结果证明了高维随机几何图团数的新下界。
We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a general lower bound applicable to various classes and study the performance of some near-optimal tests. We pay special attention to computational feasibility and construct near-optimal tests that can be computed efficiently. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.