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Thresholding projection estimators in functional linear models
"... We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as ..."
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Cited by 11 (2 self)
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We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily estimators of the derivatives of the regression function and prove they are minimax. Rates of convergence are given for some particular cases.
Single and multiple index functional regression models with nonparametric link Annals of Statistics 39
 Probability Theory: Independence, Interchangeability, Martingales (3rd ed
, 2011
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Asymptotic equivalence of functional linear regression and a white noise inverse problem
 Ann. Statist
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Continuously additive models for nonlinear functional regression
 Biometrika
, 2012
"... We introduce continuously additive models, which can be motivated as extensions of additive regression models with vector predictors to the case of infinitedimensional predictors. This approach provides a class of flexible functional nonlinear regression models, where random predictor curves are c ..."
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Cited by 5 (0 self)
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We introduce continuously additive models, which can be motivated as extensions of additive regression models with vector predictors to the case of infinitedimensional predictors. This approach provides a class of flexible functional nonlinear regression models, where random predictor curves are coupled with scalar responses. In continuously additive modeling, integrals taken over a smooth surface along graphs of predictor functions relate the predictors to the responses in a nonlinear fashion. We use tensor product basis expansions to fit the smooth regression surface that characterizes the model. In a theoretical investigation, we show that the predictions obtained from fitting continuously additive models are consistent and asymptotically normal. We also consider extensions to generalized responses. The proposed approach outperforms existing functional regression models in simulations and data illustrations.
Local linear regression for functional data, submitted
, 2008
"... We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the asymptotic mean square error. Computations involve a linear inve ..."
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Cited by 4 (2 self)
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We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the asymptotic mean square error. Computations involve a linear inverse problem as well as a representation of the small ball probability of the data and are based on recent advances in this area. The rate of convergence of our estimate outperforms those already obtained in the literature on this model.
Using basis expansions for estimating functional PLS regression. Applications with chemometric data
, 2010
"... There are many chemometric applications, such as spectroscopy, where the objective is to explain a scalar response from a functional variable (the spectrum) whose observations are functions of wavelengths rather than vectors. In this paper, PLS regression is considered for estimating the linear mode ..."
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There are many chemometric applications, such as spectroscopy, where the objective is to explain a scalar response from a functional variable (the spectrum) whose observations are functions of wavelengths rather than vectors. In this paper, PLS regression is considered for estimating the linear model when the predictor is a functional random variable. Due to the infinite dimension of the space to which the predictor observations belong, they are usually approximated by curves/functions within a finite dimensional space spanned by a basis of functions. We show that PLS regression with a functional predictor is equivalent to finite multivariate PLS regression using expansion basis coefficients as the predictor, in the sense that, at each step of the PLS iteration, the same prediction is obtained. In addition, from the linear model estimated using the basis coefficients, we derive the expression of the PLS estimate of the regression coefficient function from the model with a functional predictor. The results provided by this functional PLS approach are compared with those given by functional PCR and discrete PLS and PCR using different sets of simulated and spectrometric data.
Nonparametric estimation in functional linear models with second order stationary regressors.
, 901
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Rank tests and regression rank score tests in measurement error models
 COMPUTATIONAL STATISTICS AND DATA ANALYSIS
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