Abstract In global testing, where a large number of pointwise test statistics are aggregated to simultaneously test for a collection of null hypotheses, the handling of dependence is a crucial issue. In various fields, more particularly in genetic epidemiology and functional data analysis, many testing methods for detecting an association signal between a response and explanatory variables have been proposed. Some aggregation procedures ignore dependence across pointwise test statistics whereas others introduce a model for decorrelation, with unclear conclusions on their relative performance. Indeed, the benefit that can be expected from decorrelation highly depends on the interplay between the structure of dependence across pointwise test statistics and the pattern of the association signal. Within a large class of test statistics covering a continuum of decorrelation approaches, an optimal procedure is introduced. This procedure is based on the maximization of an ad-hoc cumulant generating function-based distance between the null and nonnull distributions of a global test statistic, in order to adapt the aggregation of the pointwise statistics to the pattern of the association signal. A comparative study including simulations and applications to genetic association studies demonstrates that the ability of this test to detect a signal is more robust to the dependence structure than existing methods.

中文翻译：

---

一种用于信号检测的自适应去相关过程

摘要 在全局测试中，大量逐点测试统计量被聚合以同时测试一组零假设，相关性的处理是一个关键问题。在各个领域，特别是在遗传流行病学和功能数据分析中，已经提出了许多用于检测响应和解释变量之间的关联信号的测试方法。一些聚合过程忽略了逐点测试统计数据的依赖性，而另一些则引入了去相关模型，对其相对性能的结论尚不清楚。实际上，可以从去相关中获得的好处在很大程度上取决于逐点测试统计数据的依赖结构与关联信号模式之间的相互作用。在涵盖一系列去相关方法的一大类测试统计数据中，引入了最佳过程。该过程基于全局测试统计的零分布和非零分布之间的基于临时累积量生成函数的距离的最大化，以便使逐点统计的聚合适应关联信号的模式。一项包括模拟和遗传关联研究应用的比较研究表明，与现有方法相比，该测试检测信号的能力对依赖结构更加稳健。该过程基于全局测试统计的零分布和非零分布之间的基于临时累积量生成函数的距离的最大化，以便使逐点统计的聚合适应关联信号的模式。一项包括模拟和遗传关联研究应用的比较研究表明，与现有方法相比，该测试检测信号的能力对依赖结构更加稳健。该过程基于全局测试统计的零分布和非零分布之间的基于临时累积量生成函数的距离的最大化，以便使逐点统计的聚合适应关联信号的模式。一项包括模拟和遗传关联研究应用的比较研究表明，与现有方法相比，该测试检测信号的能力对依赖结构更加稳健。