论文标题
通过自动统计数据的自举极限测试高维度在高维度中的显着依赖性
Testing for practically significant dependencies in high dimensions via bootstrapping maxima of U-statistics
论文作者
论文摘要
本文对测试高维矢量组件的相互独立性的问题有所不同。我们对组件消失的所有成对关联（例如所有成对的kendall $τ$）而不是测试，我们对（null） - 型号感兴趣，即所有成对关联都不超过绝对值的一定阈值。这些假设的考虑是由观察到的，即在高维度中，很少有人可以通过假设所有成对缔合恰好等于零来确切地对其进行零假设。 零假设作为综合假设的表述使得构建测试的问题是非标准的，在本文中，我们为广泛的依赖性度量提供了解决方案，可以通过$ u $统计量估算。特别是，我们为高维度中的新假设提供了渐近和引导水平$α$检验。我们还证明了新测试是最小的，并通过小型仿真研究和数据示例研究了它们的有限样本特性。
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $τ$) between the components vanish, we are interested in the (null)-hypothesis that all pairwise associations do not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in the high-dimensional regime, it is rare, and perhaps impossible, to have a null hypothesis that can be exactly modeled by assuming that all pairwise associations are precisely equal to zero. The formulation of the null hypothesis as a composite hypothesis makes the problem of constructing tests non-standard and in this paper we provide a solution for a broad class of dependence measures, which can be estimated by $U$-statistics. In particular we develop an asymptotic and a bootstrap level $α$-test for the new hypotheses in the high-dimensional regime. We also prove that the new tests are minimax-optimal and investigate their finite sample properties by means of a small simulation study and a data example.
