chapter  6
Linear Models with Functional Responses
Pages 44

In the previous chapter, we reviewed various ANOVA models for functional data. We described the pointwise, L2-norm-based, F -type, and bootstrap tests for various ANOVA models. These ANOVA models can be regarded as special functional linear models (FLMs) with functional responses and one or several categorical covariates. In this chapter, we show how these statistical tests can be extended to linear models with functional responses and some continuous covariates. Theses covariates can be time independent or dependent. When the covariates are time independent, that is, the covariates do not change over time, the associated FLMs are less involved. We deal with this case in Section 6.2 for Gaussian and non-Gaussian data. In many situations, however, the covariates can also depend on time so that the study of the associated FLMs is more involved. This case is dealt with in Section 6.3 for Gaussian data only. Technical proofs of the main results are given in Section 6.4. Some concluding remarks and bibliographical notes are given in Section 6.5. Exercises for this chapter are given in Section 6.6.