SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL

By Hervé Cardot, Frédéric Ferraty, Pascal Sarda. 2003

560 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/dbef8860aed34db5e55427e302452366c154b955

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Citations in the corpus

Testing hypotheses in the functional linear model (2003, methodology): “Indeed, let ^ be the penalized B-splines expansion estimate of the function introduced in Cardot et al. (1999b).”
Partially Linear Functional Additive Models for Multivariate Functional Data (2018, unknown): “…amount of recent work devoted to regression models with functional predictors and the most popular model is the functional linear model (James 2002; Cardot, Ferraty, and Sarda 2003; Müller and Stadtmüller 2005; Cai and Hall 2006; Crainiceanu, Staicu, and Di 2009; Li, Wang, and Carroll 2010; Cai…”
A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data (2014, background): “Functional data analysis (FDA) has become an important area of statistics research in the recent decade, see, for instance, Cardot, Ferraty, and Sarda (2003) and Cai and Hall (2006).”
Functional Adaptive Model Estimation (2005, background): “Hastie and Mallows (1993), Ramsay and Silverman (1997), Chapter 10 and Cardot et al. (2003b) discuss performing linear regression where the response is a scalar and the predictors functional.”
Regression imputation in the functional linear model with missing values in the response (2019, methodology): “Among this, the functional linear model has received a special attention (see [25, 4, 5, 3, 16, 10, 6, 31] for main references).”
Locally Sparse Estimator for Functional Linear Regression Models (2017, methodology): “For example, a smooth estimator of β(t ), proposed in Cardot, Ferraty, and Sarda (2003), is defined as β̂smooth = argmin β∈SdM { 1 n n∑ i=1 [ Yi − μ − ∫ T 0 Xi(t )β(t )dt ]2 + γ ‖Dmβ‖2 } , where Dm is the mth-order differential operator with m ≤ d, and ‖ · ‖ denotes L2 norm of a function.”
Adaptive functional linear regression (2011, background): “…appropriate choice of the weighted norm k·k ω allows us to cover the prediction problem with respect to the mean squared prediction error (see e.g. Cardot et al. [2003] or Crambes et al. [2009]) and the estimation not only of the slope function (see e.g. Hall and Horowitz [2007]) but also of its…”
Quantile regression when the covariates are functions (2005, methodology): “for instance Bosq (2000) or Cardot et al. (2003) .”
Assessing the finite dimensionality of functional data (2006, background): “…field is very extensive; it extends well into related areas, such as longitudinal data analysis, and is discussed in these books and in papers by Capra and Müller (1997), Brumback and Rice (1998), Staniswalis and Lee (1998), Cardot et al. (1999, 2003) and He et al. (2003), to list only a very few.”
Prediction in functional linear regression (2006, result): “There are a great many more recent contributions, including those of Brumback and Rice [5], Cardot [7], Cardot, Ferraty and Sarda [8, 9, 10], Girard [19], James, Hastie and Sugar [23], Boente and Fraiman [3] and He, Müller and Wang [21].”