Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 2 (2017), 3815-3840.
Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology
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.
Electron. J. Statist., Volume 11, Number 2 (2017), 3815-3840.
Received: January 2017
First available in Project Euclid: 18 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G10: Hypothesis testing 62J15: Paired and multiple comparisons
Secondary: 62P10: Applications to biology and medical sciences
Cabassi, Alessandra; Pigoli, Davide; Secchi, Piercesare; Carter, Patrick A. Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology. Electron. J. Statist. 11 (2017), no. 2, 3815--3840. doi:10.1214/17-EJS1347. https://projecteuclid.org/euclid.ejs/1508292527