One-Way anova for Functional Data via Globalizing the Pointwise F-test

In this paper, we propose and study a new global test, namely, GPF test, for the one-way anova problem for functional data, obtained via globalizing the usual pointwise F-test. The asymptotic random expressions of the test statistic are derived, and its asymptotic power is investigated. The GPF test is shown to be root-n consistent. It is much less computationally intensive than a parametric bootstrap test proposed in the literature for the one-way anova for functional data. Via some simulation studies, it is found that in terms of size-controlling and power, the GPF test is comparable with two existing tests adopted for the one-way anova problem for functional data. A real data example illustrates the GPF test.