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70
Smoothing Splines Estimators in Functional Linear Regression with ErrorsinVariables
, 2006
"... This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then ..."
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Cited by 69 (3 self)
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This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then, we adapt this estimator to the case where the covariates are noisy and we also derive an upper bound for the convergence speed. Our estimation procedure is evaluated by means of simulations.
Nonlinear estimation for linear inverse problems with error in the operator
 Annals of Statistics
"... We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove t ..."
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Cited by 31 (2 self)
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We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rateoptimality and adaptivity properties over Besov classes. 1. Introduction. Linear inverse problems with error in the operator. We want to recover f ∈ L 2 (D), where D is a domain in R d, from data (1.1) gε = Kf + ε ˙ W,
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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Bivariate splines for spatial functional regression models
 J. Nonparametr. Stat
, 2010
"... We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, with bounded or normal noise. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least square ..."
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Cited by 7 (5 self)
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We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, with bounded or normal noise. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with or without a penalization term. Under the assumptions that the regressors in the sample are bounded and span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the US that illustrates the predictive skills of the method. 1
Asymptotic equivalence of functional linear regression and a white noise inverse problem
 Ann. Statist
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Two sample inference in functional linear models
 Can. J. Statist
, 2009
"... We propose a method of comparing two functional linear models in which explanatory variables are functions (curves) and responses can be either scalars or functions. In such models, the role of parameter vectors (or matrices) is played by integral operators acting on a function space. We test the ..."
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Cited by 5 (3 self)
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We propose a method of comparing two functional linear models in which explanatory variables are functions (curves) and responses can be either scalars or functions. In such models, the role of parameter vectors (or matrices) is played by integral operators acting on a function space. We test the null hypothesis that these operators are the same in two independent samples. The complexity of the test statistics increases as we move from scalar to functional responses and relax assumptions on the covariance structure of the regressors. They all, however, have an asymptotic chi–squared distribution with the number of degrees of freedom which depends on a specific setting. The test statistics are readily computable using the R package fda, and have good finite sample properties. The test is applied to egg–laying curves of Mediterranean flies and to data from terrestrial magnetic observatories.
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.
1 Nonparametric time series forecasting with dynamic updating
"... Abstract: We present a nonparametric method to forecast a seasonal time series, and propose four dynamic updating methods to improve point forecast accuracy. Our forecasting and dynamic updating methods are datadriven and computationally fast, and they are thus feasible to be applied in practice. W ..."
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Cited by 4 (3 self)
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Abstract: We present a nonparametric method to forecast a seasonal time series, and propose four dynamic updating methods to improve point forecast accuracy. Our forecasting and dynamic updating methods are datadriven and computationally fast, and they are thus feasible to be applied in practice. We will demonstrate the effectiveness of these methods using monthly El Niño time series from 1950 to 2008