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Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology

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Cabassi, Alessandra  ORCID logo
Secchi, Piercesare 
Carter, Patrick A 


In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination methodology of Pesarin and Salmaso (2010) is used to combine all the pairwise comparisons between samples into a global test. Different combining functions and permutation strategies are reviewed and analyzed in detail. The resulting test allows to make inference on the equality of the covariance operators of multiple groups and, if there is evidence to reject the null hypothesis, to identify the pairs of groups having different covariances. It is shown that, for some combining functions, step-down adjusting procedures are available to control for the multiple testing problem in this setting. The empirical power of this new test is then explored via simulations and compared with those of existing alternative approaches in different scenarios. Finally, the proposed methodology is applied to data from wheel running activity experiments, that used selective breeding to study the evolution of locomotor behavior in mice.



non-Euclidean metrics, non-parametric combination, post-hoc analysis, quantitative genetics

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Electronic Journal of Statistics

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Institute of Mathematical Statistics
A. Cabassi was supported by the MRC (project reference MC_UP_0801/1) and by a “Tesi all’estero” scholarship from Politecnico di Milano, Italy. The authors also wish to thank The Washington State University College of Arts and Sciences, Office of International Programs and Office of Research for travel grants to P.A. Carter.