Journal Article

A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response

Febrero-Bande, Manuel, García-Portugués, Eduardo, González-Manteiga, Wenceslao

2014

Overview

This article proposes a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response. 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.

• Publisher: Taylor & Francis,American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America,Taylor & Francis Ltd
• Subject: Bootstrap/resampling / Calibration / Computer simulation / Data analysis / Datasets / Estimation methods / Functional and Longitudinal Data / Functional data / Goodness-of-fit methods / Graph theory / Inner products / Linear models / Mathematical models / Null hypothesis / Random variables / Regression analysis / Scalars / Simulations / Statistical analysis / Statistical computing / Studies