ABSTRACT
At the end of Chapter 4, we studied the one-sample problem for functional data where we described some basic hypothesis tests for functional data, including the pointwise, L2-norm-based, F -type, and bootstrap tests. In this chapter, we show how to extend these tests to more complicated designs where two or more functional samples are involved. We start with the two-sample problem for functional data. It is the simplest multi-sample problem. It allows us to understand hypothesis testing problems for functional data with more insight. Studies about one-way ANOVA and two-way ANOVA are then described in Sections 5.3 through 5.4. Technical proofs of the main results are outlined in Section 5.5. Some concluding remarks and bibliographical notes are given in Section 5.6. Section 5.7 is devoted to some exercise problems related to this chapter.
