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arXiv · 1205.6167

A goodness-of-fit test for the functional linear model with scalar response

Eduardo García-Portugués·Wenceslao González-Manteiga·Manuel Febrero-Bande
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Abstract

In this work, a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response is proposed. The test is based on a generalization to the functional framework of a previous one, designed for the goodness-of-fit of regression models with multivariate covariates using random projections. The test statistic is easy to compute using geometrical and matrix arguments, and simple to calibrate in its distribution by a wild bootstrap on the residuals. The finite sample properties of the test are illustrated by a simulation study for several types of basis and under different alternatives. Finally, the test is applied to two datasets for checking the assumption of the functional linear model and a graphical tool is introduced. Supplementary materials are available online.

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Eduardo García-Portugués, Wenceslao González-Manteiga, Manuel Febrero-Bande. 2012-05-28. A goodness-of-fit test for the functional linear model with scalar response. https://doi.org/10.1080/10618600.2013.812519

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