Functional Linear Regression
By Hervé Cardot, Pascal Sarda. 2018
38 citations recorded by the source corpus.
This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.
Subfields: Control and Systems Engineering
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In Control and Systems Engineering
- M. Febrero–Bande
- Wenceslao González-Manteiga
- Rina Friedberg
- Julie Tibshirani
- Susan Athey
- Stefan Wager
Citations in the corpus
- Local Linear Forests (2018, methodology): “Evaluating errors empirically, however, is difficult, so we supplement that with a simulation also used by Wager and Athey [2018] in evaluating causal forests and Künzel, Sekhon, Bickel, and Yu [2017], used to evaluate their meta-learner called the X-learner.”
- Nonparametric variable importance assessment using machine learning techniques (2020, unknown): “…nonparametric extensions of 𝑅 2 for kernel-based estimators, local polynomial regression, and functional regression (Doksum and Samarov, 1995; Yao et al. , 2005; Huang and Chen, 2008); the marginalized mean difference, 𝐸 𝑃 0 {𝐸 𝑃 0 (𝑌 ∣ 𝑋 = 𝑥 1 , 𝑊) − 𝐸 𝑃 0 (𝑌 ∣ 𝑋 = 𝑥 0 ,…”
- Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study (2017, background): “See Cardot and Sarda (2011) and Mas and Pumo (2011) for another surveys on functional linear regression, although from a different perspective.”