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Two-sample Tests for Functional Data Using Characteristic Functions


  • Mirosław Krzyśko
  • Łukasz Smaga Faculty of Mathematics and Computer Science, Adam Mickiewicz University


In this paper, we consider the two-sample problem for univariate and multivariate functional data. To solve this problem, we use tool of characteristic function and a basis function representation of functional data. We construct test statistics for conformity of distributions based on a weighted distance between characteristic functions of random vectors obtained in basis representation. Different weight functions result in different test statistics, whose distributions are approximated by permutation method. Testing procedures are implemented in the R program and the code is available. Simulation study shows good finite sample properties of proposed methods, while real data example illustrates the application of them.


How to Cite

Krzyśko, M., & Smaga, Łukasz. Two-sample Tests for Functional Data Using Characteristic Functions. Austrian Journal of Statistics, 50(4), 53–64. Retrieved from