Testing hypotheses in the functional linear model

By Hervé Cardot, Frédéric Ferraty, André Mas, Pascal Sarda. 2003

196 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e61c3eb66e639794907ce79bba019fed90429bf0

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In Statistics and Probability

Citations in the corpus

Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles (2010, methodology): “…for functional data is mostly concentrated on tests pertaining to the mean function (Fan and Lin 1998), as encountered, for instance, in functional linear models (Cardot et al. 2003; Cuevas, Febrero, and Fraiman 2004; Shen and Faraway 2004) or functional change detection (Berkes et al. 2009).”
Functional Additive Models (2008, result): “For this case, Cardot et al. (2003) provided consistency results and introduced a testing procedure.”
Adaptive Global Testing for Functional Linear Models (2014, methodology): “Cardot et al. (2003) proposed a method that reduces the problem to testing the linear effect of the first m coordinates in a basis expansion (e.g., functional principal components) of X and θ .”
Functional Modelling and Classification of Longitudinal Data * (2005, methodology): “The principal component functions or eigenfunctions in FDA describe the major 'Modes of Variation' of the data (Castro et al., 1986). The importance of smoothing in the estimation of functional principal components has been emphasized in Rice & Silverman (1991), Capra & Muller (1997), Boente & Fraim”
Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study (2017, methodology): “This model has been used in Cardot et al. (2003) and represents a case in which ˇ can be written exactly in terms of the first three eigenfunctions.”
Tests for Error Correlation in the Functional Linear Model (2010, methodology): “To understand the behavior of the residuals obtained from the functional linear model, the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace, estimation of the optimal subspace, and estimation of the regression kernel.”
A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response (2012, methodology): “The so called Functional Principal Component (FPC) regression estimation, proposed by Cardot et al. (1999), provide an orthogonal data–driven basis that gives the most rapidly convergent representation of the functional dataset predictor in a L2 sense (see Hall and Horowitz (2007)). Preda and Saport”