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

García‐Portugués, Eduardo; González–Manteiga, Wenceslao; Febrero–Bande, Manuel

doi:10.1080/10618600.2013.812519

Cited by 56 publications

(44 citation statements)

References 47 publications

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“…() developed and analysed tests for the nullity of the functional slope while García‐Portugués et al. () proposed a goodness‐of‐fit test for the null hypothesis of a functional linear model with scalar response. Chiou and Müller () proposed diagnostics for the model via residual processes.…”

Section: Discussionmentioning

confidence: 99%

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Febrero–Bande

Galeano

González–Manteiga

2015

Int Statistical Rev

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Functional data analysis is a field of growing importance in Statistics. In particular, the functional linear model with scalar response is surely the model that has attracted more attention in both theoretical and applied research. Two of the most important methodologies used to estimate the parameters of the functional linear model with scalar response are functional principal component regression and functional partial least-squares regression. We provide an overview of estimation methods based on these methodologies and discuss their advantages and disadvantages. We emphasise that the role played by the functional principal components and by the functional partial least-squares components that are used in estimation appears to be very important to estimate the functional slope of the model. A functional version of the best subset selection strategy usual in multiple linear regression is also analysed. Finally, we present an extensive comparative simulation study to compare the performance of all the considered methodologies that may help practitioners in the use of the functional linear model with scalar response.This section presents methods for estimating the parameters of the functional linear model with scalar response based on functional principal components.

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Section: Discussionmentioning

confidence: 99%

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Febrero–Bande

Galeano

González–Manteiga

2015

Int Statistical Rev

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“…Note also that the matrix A ij• , which is the most expensive in computation time, does not need to be computed for each bootstrap sample. All these computational properties are particularly useful in the case of high-dimensional or functional covariates, see Garca-Portugus et al (2013) for an illustration in the mean regression functional context. Table 1 shows the mean of the times required by 1000 original samples with B = 500 bootstrap replications, in units of seconds per original sample.…”

Section: Computational Aspectsmentioning

confidence: 99%

A lack-of-fit test for quantile regression models with high-dimensional covariates

Conde-Amboage

Sellero

González–Manteiga

2015

Computational Statistics & Data Analysis

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We propose a new lack-of-fit test for quantile regression models that is suitable even with high-dimensional covariates. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates. The test adapts concepts proposed by Escanciano (Econometric Theory, 22, 2006) to cope with many covariates to the test proposed by He and Zhu (Journal of the American Statistical Association, 98, 2003). To approximate the critical values of the test, a wild bootstrap mechanism is used, similar to that proposed by Feng et al. (Biometrika, 98, 2011). An extensive simulation study was undertaken that shows the good performance of the new test, particularly when the dimension of the covariate is high. The test can also be applied and performs well under heteroscedastic regression models. The test is illustrated with real data about the economic growth of 161 countries.

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“…() treat the linear model ( as the null, to be tested versus the additive model , while García‐Portugués et al. ) consider testing against a more general alternative. Horvath and Kokoszka () and Zhang et al.…”

Section: Which Methods To Choose?mentioning

confidence: 99%

“…The (restricted) likelihood ratio test of Swihart et al (2014) can be applied either to that zero-effect null or, alternatively, to the null hypothesis thatˇ.t/ is a constant-a hypothesis that, if true, allows one to regress on the across-the-function average rather than resorting to functional regression. McLean et al (2015) treat the linear model (1) as the null, to be tested versus the additive model (8), while García-Portugués et al (2014) consider testing against a more general alternative. Horvath and Kokoszka (2012) and investigate hypothesis testing procedures to choose the polynomial order in functional polynomial models such as the quadratic model (5).…”

Section: Hypothesis Testingmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

151

109

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

Cited by 56 publications

References 47 publications

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

A lack-of-fit test for quantile regression models with high-dimensional covariates

Methods for Scalar‐on‐Function Regression

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