Goodness-of-fit test for functional linear models based on integrated projections

Model must align true,
Goodness-of-fit shows the way
Functional beauty
Dimension reduction
Functional data
Functional linear models
R package
Elastic net regularization
Weather data

Eduardo García Portugués, Javier Álvarez Liébana, Gonzalo Álvarez Pérez and Wenceslao González Manteiga, «Goodness-of-fit test for functional linear models based on integrated projections», IWFOS 2020: Functional and High-Dimensional Statistics and Related Fields 107-114 (2020), doi: 10.1007/978-3-030-47756-1_15


Universidad Carlos III

Universidad Complutense de Madrid

Universidad de Oviedo

Universidad de Santiago de Compostela


June 2020

Otros detalles

Incluido como parte del Special Issue asociado al 4th Workshop on Goodness-of-Fit, Change-Point and Related Problems» celebrado en Trento en 2019



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.

Código R y datos

El código está documentado y libremente disponible en el repositorio GitHub. Además dicho software fue subido como paquete de R.

Hay dos archivos de datos incluidos en el repositorio:

Cita BibTeX

  author = {E. García-Portugués and J. Álvarez-Liébana and G. Álvarez-Pérez and W. González-Manteiga},
  title = {Goodness-of-fit Tests for Functional Linear Models Based on Integrated Projections},
  publisher = {In: Aneiros, G., Horová, I., Hušková, M., Vieu, P. (eds) Functional and High-Dimensional Statistics and Related Fields. IWFOS 2020. Contributions to Statistics. Springer, Cham},
  doi = {10.1007/978-3-030-47756-1_15},
  url = {},
  year = {2020}