García Portugués, EduardoÁlvarez Liébana, JavierÁlvarez Pérez, GonzaloGonzález Manteiga, Wenceslao2024-01-252024-01-252021García-Portugués, E. et al. (2021) «A goodness-of-fit test for the functional linear model with functional response», Scandinavian Journal of Statistics, 48(2), pp. 502-528. doi:10.1111/SJOS.12486.1467-946910.1111/SJOS.12486https://hdl.handle.net/20.500.14352/95397The 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 calibrates the test through a wild bootstrap on the residuals and the use of convenient computational procedures. As a sideways contribution, and since the statistic requires a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test is illustrated via a simulation study. Also, the new proposal is compared with previous significance tests. Two novel real data sets illustrate the application of the new test.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1111/SJOS.12486https://onlinelibrary.wiley.com/doi/10.1111/sjos.12486restricted access519.852BootstrapCramér–von Mises statisticFunctional dataGoodness-of-fitRegularizationProgramación Lineal1209.03 Análisis de Datos