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

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.

Paper: 17 pages, 2 figures, 3 tables. Supplementary material: 8 pages, 6 figures, 10 tables

References in corpus (4)

• Prediction in functional linear regression
• Methodology and convergence rates for functional linear regression
• Projection-based nonparametric goodness-of-fit testing with functional covariates
• Bootstrap independence test for functional linear models

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