%0 Journal Article
%A García Portugués, Eduardo
%A Álvarez Liébana, Javier
%A Álvarez Pérez, Gonzalo
%A González Manteiga, Wenceslao
%T A goodness-of-fit test for the functional linear model with functional response
%D 2021
%@ 1467-9469
%U https://hdl.handle.net/20.500.14352/95397
%X 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 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.
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