Two-Sample Hypothesis Test for Functional Data

In this paper, we develop and study a novel testing procedure that has more a powerful ability to detect mean difference for functional data. In general, it includes two stages: first, splitting the sample into two parts and selecting principle components adaptively based on the first half-sample; then, constructing a test statistic based on another half-sample. An extensive simulation study is presented, which shows that the proposed test works very well in comparison with several other methods in a variety of alternative settings.