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Adaptive Functional Linear Regression
"... Theoretical results in the functional linear regression literature have so far focused on minimax estimation where smoothness parameters are assumed to be known and the estimators typically depend on these smoothness parameters. In this paper we consider adaptive estimation in functional linear regr ..."
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Cited by 1 (0 self)
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Theoretical results in the functional linear regression literature have so far focused on minimax estimation where smoothness parameters are assumed to be known and the estimators typically depend on these smoothness parameters. In this paper we consider adaptive estimation in functional linear
Prediction in functional linear regression
, 2006
"... There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finitedimensional regression, much of the practical interest in the slope centers on its application for the purpose of ..."
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Cited by 70 (5 self)
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There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finitedimensional regression, much of the practical interest in the slope centers on its application for the purpose
VaryingCoefficient Functional Linear Regression
"... Abstract: Functional linear regression analysis aims to model regression relations which include a functional predictor. The analogue to the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one or t ..."
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Abstract: Functional linear regression analysis aims to model regression relations which include a functional predictor. The analogue to the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one
PREDICTION IN FUNCTIONAL LINEAR REGRESSION
"... There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finitedimensional regression, much of the practical interest in the slope centers on its application for the purpose of ..."
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There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finitedimensional regression, much of the practical interest in the slope centers on its application for the purpose
Functional linear regression with derivatives
"... We introduce a new model of linear regression for random functional inputs taking into account the rst order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronized pena ..."
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We introduce a new model of linear regression for random functional inputs taking into account the rst order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronized
CLT in functional linear regression models
 Probab. Theory Related Fields
, 2007
"... We propose in this work to derive a CLT in the functional linear regression model. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of illposed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first ..."
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Cited by 9 (1 self)
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We propose in this work to derive a CLT in the functional linear regression model. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of illposed inverse problem. We consider estimators that belong to a large class of regularizing methods and we
From Multivariate to Functional Linear Regression
, 2005
"... The aim of this contribution is to present a new, however rapidly developing domain of statistics – functional data analysis (FDA). A particular problem of extending multivariate regression to the functional setting is discussed. First of all, two real data sets and connected problems are presented ..."
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are presented. Multivariate regression is briefly recalled focusing mainly on the case of strongly correlated predictors and its disadvantages for FDA. A direct (naive) approach from the multivariate to the functional setting is then mentioned. Finally, a functional linear regression model is introduced and two
Methodology and convergence rates for functional linear regression
, 2007
"... In functional linear regression, the slope “parameter ” is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an illposed problem and has points of contact with a range of methodologies, including statistical smoothi ..."
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Cited by 75 (7 self)
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In functional linear regression, the slope “parameter ” is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an illposed problem and has points of contact with a range of methodologies, including statistical
Functional linear regression analysis for longitudinal data
 Ann. of Statist
, 2005
"... We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small number ..."
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Cited by 65 (7 self)
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We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small
Results 1  10
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2,763,435