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Abstract:
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We propose a new approach to the problem of one-way ANOVA for functional data based on basis expansion and our recent development of multiplier bootstrap for high-dimensional data with weak variance decay. We show that, the test not only admits the root-n consistency, but also has a size of a nearly parametric rate. Numerically, we demonstrate that it is comparable to existing tests in general situations, while exhibits a clear advantage when the problem is hard in the sense that the functional data are rough and/or the signals are weak.
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