Structural test in regression on functional variables

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

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“…Delsol et al. ) propose a test for the null hypothesis that m in the non‐parametric model ( belongs to a given family of operators.…”

Section: Which Methods To Choose?mentioning

confidence: 99%

“…Horvath and Kokoszka (2012) and investigate hypothesis testing procedures to choose the polynomial order in functional polynomial models such as the quadratic model (5). Delsol et al (2011) propose a test for the null hypothesis that m in the non-parametric model (9) belongs to a given family of operators.…”

Section: Hypothesis Testingmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

146

109

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“…Recently, Xu et al (2011) discussed an F-test in a linear longitudinal data model, and Kokoszka et al (2008) tested for lack of dependence in a functional linear model where both the response and the predictor are curves. Delsol et al (2011) proposed a theoretical framework for structural testing procedures adapted to functional regression. In practice, one may be interested in whether certain explanatory variables in the parametric components influence the response significantly.…”

Section: Introductionmentioning

confidence: 99%

A test of linearity in partial functional linear regression

Zhang

2016

Metrika

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This paper investigates the hypothesis test of the parametric component in partial functional linear regression. We propose a test procedure based on the residual sums of squares under the null and alternative hypothesis, and establish the asymptotic properties of the resulting test. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, we present an illustration through fitting the Berkeley growth data with a partial functional linear regression model and testing the effect of gender on the height of kids.

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“…In addition to the GoF proposals for the FLMSR discussed above, Delsol et al (2011) formulated a kernel-based test for model assumptions, whereas Bücher et al (2011) introduced testing procedures well-adapted for the time-variation of directional profiles. Generalized likelihood ratio tests were suggested in McLean et al (2015) to test the linearity of functional generalized additive models.…”

Section: Introductionmentioning

confidence: 99%

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

García‐Portugués¹,

González–Manteiga²,

Febrero–Bande³

2014

Journal of Computational and Graphical Statistics

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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.

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Structural test in regression on functional variables

Abstract: International audienc

Cited by 39 publications

References 59 publications

Methods for Scalar‐on‐Function Regression

Methods for Scalar‐on‐Function Regression

A test of linearity in partial functional linear regression

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

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