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A functional generalized F‐test for signal detection with applications to event‐related potentials significance analysis
Author(s) -
Causeur David,
Sheu ChingFan,
Perthame Emeline,
Rufini Flavia
Publication year - 2020
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13118
Subject(s) - pointwise , statistical hypothesis testing , functional data analysis , statistics , null hypothesis , test statistic , population , mathematics , null distribution , computer science , mathematical analysis , demography , sociology
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.