Open Access
2017 Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology
Alessandra Cabassi, Davide Pigoli, Piercesare Secchi, Patrick A. Carter
Electron. J. Statist. 11(2): 3815-3840 (2017). DOI: 10.1214/17-EJS1347


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.


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Alessandra Cabassi. Davide Pigoli. Piercesare Secchi. Patrick A. Carter. "Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology." Electron. J. Statist. 11 (2) 3815 - 3840, 2017.


Received: 1 January 2017; Published: 2017
First available in Project Euclid: 18 October 2017

zbMATH: 06796556
MathSciNet: MR3714299
Digital Object Identifier: 10.1214/17-EJS1347

Primary: 62G10 , 62J15
Secondary: 62P10

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

Vol.11 • No. 2 • 2017
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