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Title: An ANOVA test for functional data with graphical interpretation Authors:  Tomas Mrkvicka - University of South Bohemia (Czech Republic) [presenting]
Mari Myllymaki - Natural Resources Institute Finland (Finland)
Ute Hahn - University of Aarhus (Denmark)
Abstract: A new functional ANOVA test, with a graphical interpretation of the result, will be presented. The test is an extension of a global envelope test recently introduced. The graphical interpretation is realized by a global envelope which is drawn jointly for each sample of functions. If an average function, computed over a sample, is out of the given envelope, the null hypothesis is rejected with the predetermined significance level $\alpha$. The advantages of the proposed procedure are that it identifies the domains of the functions which are responsible for the potential rejection and that it immediately offers a post-hoc test by identifying the samples which are responsible for the potential rejection. All that is done at an exact significance level $\alpha$. Our simulations show that the power of the test also tends to be higher than the power of recently available procedures.