Testing for No Effect in Functional Linear Regression Models, Some Computational Approaches

Cardot, Hervé; Goia, Aldo; Sarda, Pascal

doi:10.1081/sac-120028440

Cited by 33 publications

(26 citation statements)

References 10 publications

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“…As discussed by Cardot and colleagues [8][9][10], a functional linear model offers a natural extension of traditional linear models. Theoretically, within the framework of functional linear models, the effects of predictors to the response curves can be estimated and accordingly the hypotheses can be tested via comparison of nested models.…”

Section: Introductionmentioning

confidence: 97%

Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data

Yang

Nie

2007

Statistics in Medicine

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Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.

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Section: Introductionmentioning

confidence: 97%

Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data

Yang

Nie

2007

Statistics in Medicine

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“…For example, Cardot et al [7], Müller and Stadtmüller [23] and Cardot et al [8] considered the problem of testing a simple hypothesis in the case where the response is real and the predictor is a random function, while Mas [22] investigated a test for the mean of random curves. Recently, Shen and Faraway [29] and Yang et al [31] discussed an F -test in a linear longitudinal data model, while Kokoszka et al.…”

Section: Introductionmentioning

confidence: 98%

Testing model assumptions in functional regression models

Bücher¹,

Dette²,

Wieczorek³

2011

Journal of Multivariate Analysis

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a b s t r a c tIn the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L 2 -distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite sample properties of the tests are illustrated by means of a small simulation study. It is also demonstrated that for small samples, bootstrap versions of the tests improve the quality of the approximation of the nominal level.

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“…Despite the abundant literature devoted to functional regression models and structural testing procedures in multivariate regression, there are very few papers on structural testing procedures in functional regression. As far as we know the existing literature is reduced to papers dealing with tests for no-effect (see for instance [40]) or tests of H 0 : {r = r 0 } (where r 0 is a known operator) in the functional linear model (see for instance [7,8], or [59]). Recently, a heuristic goodness of fit test based on functional principal components decomposition has been proposed in [12].…”

Section: Introductionmentioning

confidence: 99%