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B0850
**Title: **Testing the equality of a large number of means of functional data
**Authors: **Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain) **[presenting]**

**Abstract: **Given $k$ independent samples of functional data, the problem of testing for the equality of their mean functions is considered. In contrast to the classical setting where $k$ is fixed and the sample size from each population increases without bound, $k$ is assumed to be large and the size of each sample is either bounded or small in comparison to $k$. The asymptotic distribution of the considered test statistic is studied under the null hypothesis of equality of the $k$ mean functions as well as under alternatives.