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A symmetry test for functional data via the empirical characteristic functional

Author

Listed:
  • Hedvika Ranošová

    (Charles University)

  • Daniel Hlubinka

    (Charles University)

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.

Suggested Citation

  • Hedvika Ranošová & Daniel Hlubinka, 2025. "A symmetry test for functional data via the empirical characteristic functional," Statistical Papers, Springer, vol. 66(5), pages 1-23, August.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01716-8
    DOI: 10.1007/s00362-025-01716-8
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