Inter-subject Correlation Analysis for Functional Data with Applications to fMRI Studies

A focus of the inter-subject correlation (ISC) analysis is to understand the correlation among individuals’ brain activities to identify the brain regions that respond similarly to the same real-life stimuli. We explore the benefit of using nonparametric smoothing in the ISC test and propose a nonparametric test procedure for testing the existence of the inter-subject correlation. More specifically, testing whether the covariance matrix among subjects is diagonal. Our proposed test is applicable under subject heteroscedasticity and temporal heteroscedasticity with no temporal dependence. We also propose another nonparametric test procedure to improve the power performance and extend it to the temporal dependent case. We establish the asymptotic normality of the three proposed test statistics under the null hypothesis and a series of local alternative hypotheses, we also study their detectable order under local alternatives. Numerical studies show that the proposed test procedures perform better than the commonly used methods in the ISC studies and cross-sectional dependence tests including the adjusted Lagrange multiplier test, Pesaran’s cross sectional dependence (CD) test, and the adjusted Pesaran’s CD test. Finally we apply our proposed test statistics to a real movie-watching fMRI data set to find the brain nodes of the participants which have no inter-subject correlation for a period of time when they are watching the same movie.