Open Access
2022 Multi-sample comparison using spatial signs for infinite dimensional data
Joydeep Chowdhury, Probal Chaudhuri
Author Affiliations +
Electron. J. Statist. 16(2): 4636-4678 (2022). DOI: 10.1214/22-EJS2054


We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose a test based on spatial signs. We develop an asymptotic implementation as well as a bootstrap implementation and a permutation implementation of this test and investigate their size and power properties. We compare the performance of our test with that of several mean based tests of analysis of variance for functional data studied in the literature. Interestingly, our test not only outperforms the mean based tests in several non-Gaussian models with heavy tails or skewed distributions, but in some Gaussian models also. Further, we also compare the performance of our test with the mean based tests in several models involving contaminated probability distributions. Finally, we demonstrate the performance of these tests in three real datasets: a Canadian weather dataset, a spectrometric dataset on chemical analysis of meat samples and a dataset on orthotic measurements on volunteers.


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Joydeep Chowdhury. Probal Chaudhuri. "Multi-sample comparison using spatial signs for infinite dimensional data." Electron. J. Statist. 16 (2) 4636 - 4678, 2022.


Received: 1 June 2021; Published: 2022
First available in Project Euclid: 27 September 2022

arXiv: 2207.12025
MathSciNet: MR4489237
zbMATH: 07603095
Digital Object Identifier: 10.1214/22-EJS2054

Primary: 62R10
Secondary: 62J10

Keywords: Analysis of variance , Bootstrap test , functional data , Gaussian process , Kruskal-Wallis test , Permutation test , t process

Vol.16 • No. 2 • 2022
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