A functional generalized F‐test for signal detection with applications to event‐related potentials significance analysis

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.