Projection-based High-dimensional Sign Test
Projection-based High-dimensional Sign Test
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DOI：
10.1007/s10114-022-0435-9
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Hui Chen;Changhao Zou;Run Ze Li
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文献类型：
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作者：
Hui Chen;Changhao Zou;Run Ze Li
本文研究的是高维位置测试问题。对于高维设置，传统的基于多变量符号的测试表现不佳或变得不可行，因为它们的I型错误率远离标称水平。已经提出了一些修改来解决这个具有挑战性的问题，并显示出良好的性能。然而，大多数改进的基于符号的测试放弃了所有的相关性信息，这在某些情况下会导致功率损失。我们提出一个投影加权符号测试，以利用相关信息。在较弱的条件下，我们得到了使投影检验具有渐近和局部最优功效的最优方向和权值。受益于使用样本分裂的想法来估计最佳方向，所提出的测试能够很好地保留I型错误率与渐近分布，同时它在鲁棒性方面也具有很强的竞争力。数值模拟和一个真实的数据实例表明了该方法相对于现有方法的优越性。
This article is concerned with the high-dimensional location testing problem. For high-dimensional settings, traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels. Several modifications have been proposed to address this challenging issue and shown to perform well. However, most of modified sign-based tests abandon all the correlation information, and this results in power loss in certain cases. We propose a projection weighted sign test to utilize the correlation information. Under mild conditions, we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under alternatives. Benefiting from using the sample-splitting idea for estimating the optimal direction, the proposed test is able to retain type-I error rates pretty well with asymptotic distributions, while it can be also highly competitive in terms of robustness. Its advantage relative to existing methods is demonstrated in numerical simulations and a real data example.