A goodness‐of‐fit test for the functional linear model with functional response

@article{GarciaPortugues2019AGT,
  title={A goodness‐of‐fit test for the functional linear model with functional response},
  author={Eduardo Garc'ia-Portugu'es and Javier 'Alvarez-Li'ebana and Gonzalo {\'A}lvarez‐P{\'e}rez and Wenceslao Gonz'alez-Manteiga},
  journal={Scandinavian Journal of Statistics},
  year={2019},
  volume={48},
  pages={502 - 528}
}
The functional linear model with functional response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this article, we propose a novel goodness‐of‐fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramér–von Mises norm over a doubly projected empirical process which, using geometrical arguments, yields an easy‐to‐compute weighted quadratic norm. A resampling procedure… 
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