28. Oct 2025

Daniel Hlubinka

15:45 h

Abstract: Characteristic functions are a popular tool for constructing various tests for functional data. Using the Cramér-von Mises kind of test statistic we can use a specific form of the characteristic function under the null hypothesis, and the constructing the test is then relatively straightforward. Unfortunately, the critical values of such tests must be approximated using a resampling method such as bootstrap or using a permutation principle. We show, that using a Gaussian measure in the construction of the Cramér-von Mises test statistic simplifies the statistic such that there is no need to estimate an integral with respect to some probability measure on the set of square integrable functions. Moreover, the versatility of the covariance operators of Gaussian processes allow to focus on the power of the test with respect to a specific alternatives. In particular, we show functional ANOVA and test of symmetry for functional data.