Goodness-of-fit Tests for Functional Linear Models Based on Integrated Projections

  • Eduardo García-PortuguésEmail author
  • Javier álvarez-Liébana
  • Gonzalo álvarez-Pérez
  • Wenceslao González-Manteiga
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with functional response that neatly adapts to functional/scalar responses/predictors. In particular, the new goodness-of-fit test extends a previous proposal for scalar response. The test statistic is based on a convenient regularized estimator, is easy to compute, and is calibrated through an efficient bootstrap resampling. A graphical diagnostic tool, useful to visualize the deviations from the model, is introduced and illustrated with a novel data application. The R package goffda implements the proposed methods and allows for the reproducibility of the data application.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Eduardo García-Portugués
    • 1
    Email author
  • Javier álvarez-Liébana
    • 2
  • Gonzalo álvarez-Pérez
    • 3
  • Wenceslao González-Manteiga
    • 4
  1. 1.Department of Statistics and UC3M-Santander Big Data InstituteCarlos III University of MadridLeganésSpain
  2. 2.Department of Statistics and Operations Research and Mathematics DidacticsUniversity of OviedoOviedoSpain
  3. 3.Department of PhysicsUniversity of OviedoOviedoSpain
  4. 4.Department of Statistics, Mathematical Analysis and OptimizationUniversity of Santiago de CompostelaSantiago de CompostelaSpain

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