A goodness-of-fit test for the functional linear model with functional response Articles uri icon

publication date

  • June 2021

start page

  • 1

end page

  • 27

International Standard Serial Number (ISSN)

  • 0303-6898

Electronic International Standard Serial Number (EISSN)

  • 1467-9469


  • 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&;8208#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.


  • Statistics


  • bootstrap; cramér-von mises statistic; functional data,goodness-of-fit; regularization