Electronic Journal of Statistics

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

Alessandra Cabassi, Davide Pigoli, Piercesare Secchi, and Patrick A. Carter

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Abstract

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.

Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 3815-3840.

Dates
Received: January 2017
First available in Project Euclid: 18 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1508292527

Digital Object Identifier
doi:10.1214/17-EJS1347

Mathematical Reviews number (MathSciNet)
MR3714299

Zentralblatt MATH identifier
06796556

Subjects
Primary: 62G10: Hypothesis testing 62J15: Paired and multiple comparisons
Secondary: 62P10: Applications to biology and medical sciences

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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


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