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Abstract:
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The motivation of the present work is to build statistical methodology for testing equality of functional data across groups. We concentrate on testing equality of the data structures based on latent components. Without much knowledge of data, bootstrapping and other data-driven testing procedures are considered, and we use Monte Carlo study to compare expected and empirical rejection levels. We use Kolmogorov-Smirnov type statistics to test equality of marginal distributions of two or more stationary processes, and use spectral domain methods to develop a testing procedure for testing equality of second order dependence in those processes. In practice, we need the test to be robust against non-normal data, unknown dependence structure, different number of variables per group and unequal group sample sizes. The proposed methods are illustrated in real fMRI data analysis.
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