A symmetry test for functional data via the empirical characteristic functional

Hedvika Ranošová () and Daniel Hlubinka ()
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Hedvika Ranošová: Charles University
Daniel Hlubinka: Charles University

Statistical Papers, 2025, vol. 66, issue 5, No 3, 23 pages

Abstract: Abstract A test of central symmetry of a functional random variable is proposed. We use the characterization of symmetry via the characteristic functional, that is, we use the fact that the characteristic functional of a symmetric random function is a real-valued functional. Hence, we construct a Cramér–von Mises-type test of the hypothesis that the imaginary part of the characteristic functional vanishes. The test statistic assumes a relatively simple form if we use a Gaussian measure to construct the test. As the test statistic is a degenerate U-statistic, we must use a wild bootstrap to obtain approximate critical values under the null hypothesis. An alternative approach based on a two-sample test for functional data is compared with our test procedure. Several simulations illustrate the performance of the proposed test.

Keywords: Functional data analysis; Symmetry; Characteristic functional; 62G10; 62R10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01716-8

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