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

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 resp...

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Bibliographic Details
Published in:arXiv.org 2020-08
Main Authors: García-Portugués, Eduardo, Álvarez-Liébana, Javier, Álvarez-Pérez, Gonzalo, González-Manteiga, Wenceslao
Format: Article
Language:English
Subjects:
Diagnostic software
Diagnostic systems
Goodness of fit
Random variables
Resampling
Statistical tests
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2008.09885