An anova test for functional data

Given k independent samples of functional data the problem of testing the null hypothesis of equality of their respective mean functions is considered. So the setting is quite similar to that of the classical one-way anova model but the k samples under study consist of functional data. A simple natural test for this problem is proposed. It can be seen as an asymptotic version of the well-known anova F-test. The asymptotic validity of the method is shown. A numerical Monte Carlo procedure is proposed to handle in practice the asymptotic distribution of the test statistic. A simulation study is included and a real-data example in experimental cardiology is considered in some detail. c © 2003 Elsevier B.V. All rights reserved.