Linear functional regression: The case of fixed design and functional response

By Antonio Cuevas, M. Febrero, Ricardo Fraiman. 2002

184 citations recorded by the source corpus.

The authors consider the problem of simple linear regression when the exogenous and endogenous variables are functional and the design is fixed. They propose an estimator for the underlying linear operator and prove its consistency under some conditions which ensure that the design is sufficiently informative. They consider the classical calibration (or inverse regression) problem and analyze a consistent estimator. They also give a simulation study. The proposed method is not hard to implement in practice.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b4491dc5a3e16f4ccb34eb26441d1dca88fe0f20

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Asymptotics of prediction in functional linear regression with functional outputs (2009, background): “When turning to the predictor, (11) may be enhanced : Ŝn (Xn+1)− S (Xn+1) (12)”
Smoothing splines estimators for functional linear regression (2009, background): “As pointed out by several authors (Marx and Eilers [22], Ramsay and Silverman [26] or Cuevas, Febrero and Fraiman [10]) the use of functional models for these settings has some advantages over discrete, multivariate approaches.”
Functional Modelling and Classification of Longitudinal Data * (2005, methodology): “In the functional regression model (Ramsay & Dalzell, 1991; Cardot et al., 1999, 2003; Cuevas et al., 2002 ) it is assumed that both predictor and response are random functions.”
Functional linear regression analysis for longitudinal data (2005, background): “The theory for the case of fixed design and functional response in the densely sampled case was investigated by Cuevas, Febrero and Fraiman [8].”
Partially functional linear regression in high dimensions (2016, methodology): “…regression is widely used to model the prediction of a functional predictor through a linear operator, often realized via an integral form of a regression parameter function; see Ramsay & Dalzell (1991), Cuevas et al. (2002), Cardot et al. (2003), Ramsay & Silverman (2005) and Yao et al. (2005a).”
CLT in functional linear regression models (2005, methodology): “Diﬀerent estimators for the functional parameter have been considered in the functional linear regression model: see for instance Goutis (1998), Cuevas et al. (2002) and Cardot et al. (1999, 2003).”
Functional linear regression with functional response (2017, background): “Cuevas, Febrero, and Fraiman (2002) consider a xed design setting and propose an estimator of based on interpolation.”
Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, methodology): “, 2007), and dealing with the case where the dependent variables are curves as well (Cuevas et al., 2002; Lian, 2007).”
DEPENDENT FUNCTIONAL LINEAR MODELS WITH APPLICATIONS TO MONITORING STRUCTURAL CHANGE (2014, unknown): “(1996), Horváth et al. (2004) and Aue et al.”