ABSTRACT
In Chapter 5, various ANOVA models were studied under the equal-covariance function (ECF) assumption. When this ECF assumption is not satisfied, various heteroscedastic ANOVA models were studied in Chapter 9. In this chapter, we study how to test if two or several functional samples have the same covariance function. That is, we aim to test if the ECF assumption is valid for the functional samples involved in a functional ANOVA model. We start with the two-sample case (Zhang and Sun 2010) in Section 10.2. The methodologies are then extended for multi-sample cases (Zhang 2013b) in Section 10.3. Technical proofs of the main results are outlined in Section 10.4. Some concluding remarks and bibliographical notes are given in Section 10.5. Section 10.6 is devoted to some exercise problems related to this chapter.
