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Measuring and Testing Mutual Dependence of Multivariate Functional Data

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Krzyśko M., Smaga Ł.
Statistics in Transition new series
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2020
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vol. 21
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issue 3
21-37
EN
This paper considers new measures of mutual dependence between multiple multivariate random processes representing multidimensional functional data. In the case of two processes, the extension of functional distance correlation is used by selecting appropriate weight function in the weighted distance between characteristic functions of joint and marginal distributions. For multiple random processes, two measures are sums of squared measures for pairwise dependence. The dependence measures are zero if and only if the random processes are mutually independent. This property is used to construct permutation tests for mutual independence of random processes. The finite sample properties of these tests are investigated in simulation studies. The use of the tests and the results of simulation studies are illustrated with an example based on real data.
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Functional repeated measures analysis of variance and its application

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Kuryło K., Smaga Ł.
Statistics in Transition new series
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2024
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vol. 25
|
issue 2
185-204
EN
This paper is inspired by medical studies in which the same patients with multiple sclerosis are examined at several successive visits (doctor’s appointments) and described by fractional anisotropy tract profiles, which can be represented as f unctions. Since the observations for each patient are dependent random processes, they follow a repeated measures design for functional data. To compare the results for different visits, we thus consider functional repeated measures analysis of variance. For this purpose, a pointwise test statistic is constructed by adapting the classical test statistic for one-way repeated measures analysis of variance to the functional data framework. By integrating and taking the supremum of the pointwise test statistic, we create two global test statistics. In addition to verifying the general null hypothesis of the equality of mean functions corresponding to different objects, we also propose a simple method for post hoc analysis. We illustrate the finite sample properties of permutation and bootstrap testing procedures in an extensive simulation study. Finally, we analyze a real data example in detail. All methods are implemented in the R package rmfanova, available on CRAN.
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