Presmoothing in functional linear regression

Ferraty, Frédéric; González–Manteiga, Wenceslao; Martínez-Calvo, Adela; Vieu, Philippe

doi:10.5705/ss.2010.085

Cited by 39 publications

(35 citation statements)

References 21 publications

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“…() introduced techniques based on canonical analysis; Yuan and Cai () suggested a method founded on reproducing kernel Hilbert space analysis; Ferraty et al . () discussed presmoothing methods; and Comte and Johannes (), Johannes and Schenk () and Cai and Zhou () treated methods for adaptive smoothing in functional linear regression. Fan and Zhang (), Yao et al .…”

Section: Introductionmentioning

confidence: 99%

Truncated Linear Models for Functional Data

Hall

Hooker

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Abstract. A conventional linear model for functional data involves expressing a response variable Y in terms of the explanatory function X(t), via the model: Y = a + I b(t) X(t) dt + error, where a is a scalar, b is an unknown function and I = [0, α] is a compact interval. However, in some problems the support of b or X, I 1 say, is a proper and unknown subset of I, and is a quantity of particular practical interest. In this paper, motivated by a real-data example involving particulate emissions, we develop methods for estimating I 1 . We give particular emphasis to the case I 1 = [0, θ], where θ ∈ (0, α], and suggest two methods for estimating a, b and θ jointly; we introduce techniques for selecting tuning parameters; and we explore properties of our methodology using both simulation and the real-data example mentioned above. Additionally, we derive theoretical properties of the methodology, and discuss implications of the theory. Our theoretical arguments give particular emphasis to the problem of identifiability.

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Section: Introductionmentioning

confidence: 99%

Truncated Linear Models for Functional Data

Hall

Hooker

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Such data are known in the literature as functional data (Bongiorno et al 2014;Ferraty and Vieu 2006;Horváth and Kokoszka 2012;Ramsay and Silverman 2005). Examples of functional data can be found in various application domains, such as medicine, economics, meteorology and many others.…”

Section: Introductionmentioning

confidence: 99%

“…Methods of functional data analysis are becoming increasingly popular, e.g. in the cluster analysis (Jacques and Preda 2013;James and Sugar 2003;Peng and Müller 2008), classification (Chamroukhi et al 2013;Delaigle and Hall 2012;Mosler and Mozharovskyi 2015;Rossi and Villa 2006) and regression (Ferraty et al 2012;Goia and Vieu 2014;Kudraszow and Vieu 2013;Peng et al 2015;Rachdi and Vieu 2006;Wang et al 2015). Unfortunately, multivariate data methods cannot be directly used for functional data, because of the problem of dimensionality and difficulty in putting functional data into order.…”

Section: Introductionmentioning

confidence: 99%

Selected statistical methods of data analysis for multivariate functional data

et al. 2016

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Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92-106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

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“…A reasonably accurate estimation of principal components might explain why this occurred in our example over the prediction period September 5–14. Finally, Ferraty et al () considered pre‐smoothing for FPCR, that is the perturbation of the normal equation Γ g = Δ at the beginning of the analysis. It seems to significantly improve the FPCR when the sample size is small or the noise is large.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Bivariate splines for ozone concentration forecasting

2012

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In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with penalty to the principal components regression approach. Moderate sample sizes provide good quality forecasts in both cases with little computational effort. We also illustrate the variability of forecasts owing to the choice of smoothing penalty. Finally, we compare our predictions with the ones obtained using thin‐plate splines. Predictions based on bivariate splines require less computational time than the ones based on thin‐plate splines and are more accurate. We also quantify the variability in the predictions arising from the variability in the sample using the jackknife, and report that predictions based on bivariate splines are more robust than the ones based on thin‐plate splines. Copyright © 2012 John Wiley & Sons, Ltd.

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Presmoothing in functional linear regression

Cited by 39 publications

References 21 publications

Truncated Linear Models for Functional Data

Truncated Linear Models for Functional Data

Selected statistical methods of data analysis for multivariate functional data

Bivariate splines for ozone concentration forecasting

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