IRMAR UMR CNRS 6625, Agrocampus Ouest, Rennes Cedex, France.
Institute of Education, National Cheng Kung University, Tainan, Taiwan.
Biometrics. 2020 Mar;76(1):246-256. doi: 10.1111/biom.13118. Epub 2019 Oct 17.
Motivated by the analysis of complex dependent functional data such as event-related brain potentials (ERP), this paper considers a time-varying coefficient multivariate regression model with fixed-time covariates for testing global hypotheses about population mean curves. Based on a reduced-rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F-test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control.
受分析复杂相关功能数据（如事件相关脑电位 [ERP]）的启发，本文考虑了一个具有固定时间协变量的时变系数多元回归模型，用于检验关于总体均值曲线的全局假设。基于对逐点检验统计量的随机过程时间相关性的降秩建模，提出了一种功能广义 F 检验，并推导出其渐近零分布。我们的分析结果表明，与依赖数据的功能方差分析检验方法和竞争信号检测程序相比，该检验具有更高的功效。模拟研究证实了这种功效增益对于与 ERP 中观察到的类似的相关模式的数据。新的检验程序通过对冲动控制神经相关研究的 ERP 数据进行分析来说明。
