Andrii Babii, Marine Carrasco, Idriss Tsafack
arXiv 16 Feb 2024 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2025) · 1 citations (OpenAlex)
arXiv:2402.11134 · PDF · DOI · OpenAlex · Extracted main text
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains nearly minimax-optimal convergence rates over a class of ellipsoids and propose an adaptive early stopping procedure for selecting the number of PLS components. In addition, we develop new test that can detect local alternatives converging at the parametric rate which can be inverted to construct confidence sets. Simulation results demonstrate that the estimator performs favorably relative to several existing methods and the proposed test exhibits good power properties. We apply our methodology to evaluate the nonlinear effects of temperature on corn and soybean yields.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Heinz Werner Engl, Martin Hanke, and Andreas Neubauer (1996) Regularization of inverse problems, volume 375 | 1.000 | 9 | 5 | 100% |
| 2 | Aurore Delaigle and Peter Hall (2012) Methodology and theory for partial least squares applied to functional data | 1.000 | 6 | 4 | 100% |
| 3 | Martin Hanke (1995) Conjugate gradient type methods for linear ill-posed problems | 1.000 | 6 | 4 | 100% |
| 4 | Wolfram Schlenker and Michael J Roberts (2009) Nonlinear temperature effects indicate severe damages to us crop yields under climate change | 0.874 | 7 | 2 | 100% |
| 5 | T Tony Cai and Ming Yuan (2012) Minimax and adaptive prediction for functional linear regression | 0.843 | 3 | 3 | 100% |
| 6 | Naveen Gupta, S Sivananthan, and Bharath K Sriperumbudur (2023) Convergence analysis of kernel conjugate gradient for functional linear regression | 0.843 | 3 | 3 | 100% |
| 7 | Christophe Crambes, Alois Kneip, and Pascal Sarda (2009) Smoothing splines estimators for functional linear regression | 0.811 | 4 | 2 | 100% |
| 8 | Peter Hall and Joel L Horowitz (2007) Methodology and convergence rates for functional linear regression | 0.737 | 3 | 2 | 100% |
| 9 | Ming Yuan and T Tony Cai (2010) A reproducing kernel hilbert space approach to functional linear regression | 0.737 | 3 | 2 | 100% |
| 10 | Alexandre B Tsybakov (2009) Introduction to nonparametric estimation | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 52 scored citations.