A1078
Title: Goodness-of-fit and distribution tests for functional data
Authors: Daniel Hlubinka - Univerzita Karlova (Czech Republic) [presenting]
Abstract: The aim is to present a method for constructing tests using empirical characteristic functionals to test the distribution of functional random variables. In particular, a goodness-of-fit test and a test of symmetry and time reversibility for continuous stochastic processes are presented. Characteristic functionals can be used to construct distance-based tests for distribution or distributional properties of functional data. This approach is particularly useful because the characteristic functional can be consistently estimated, and test statistics are derived as if the functions were fully observable. Once constructed, the test statistics are adjusted because the underlying functions are only observed at a discrete grid. Typically, the Cramer-von Mises test statistic is employed, which is based on the integrated distance between the empirical characteristic functional and its counterpart under the null hypothesis. As the exact distribution of the test statistic under the null hypothesis is unknown and the asymptotic distribution is usually very complicated, some resampling or subsampling methods are used to derive the critical values for the test. The choice of probability distribution for the Cramer-von Mises statistic is also discussed, and the performance of the tests is demonstrated under the null hypothesis and various alternatives.
