The paper introduces a pooling‑ridge estimation method for functional linear regression that handles data observed at discrete times, ranging from sparse to dense designs. By combining pooling strategies with RKHS‑based techniques, the authors achieve minimax‑optimal prediction risk for both scalar‑on‑function and function‑on‑function models. The study identifies distinct phase transitions in convergence behavior, with up to three transitions for function‑on‑function regression, and validates the approach through simulations and real data examples.
By Shunxing Yan, Fang Yao
arXiv:2511. 15615v2 Announce Type: replace-cross Abstract: This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate.
By G\'abor Bal\'azs
arXiv:2411.09686v4 Announce Type: replace
Abstract: Regressing a function $F$ on $\mathbb{R}^d$ without incurring the statistical and computational curse of dimensionality requires exploitable struct...
By Yantao Wu, Mauro Maggioni
arXiv:2504.18184v5 Announce Type: replace
Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
By Jia-Qi Yang, Lei Shi
arXiv:2608. 15121v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) seeks the minimal subspace of the predictors that captures the full conditional distribution of the response, which is known as the central subspace (CS).
By Ye Tian
arXiv:2507. 20975v5 Announce Type: replace-cross Abstract: Operator models are regression algorithms between Banach spaces of functions.
By Trevor Harris, Yan Liu
arXiv:2608. 06340v1 Announce Type: cross Abstract: Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series.
By Daniel Paulin, Victor Elvira
Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags.
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti
The paper introduces a new inference framework for least angle regression (LAR), clarifying its behavior and providing a formal stopping rule. It shows that LAR estimates non‑zero population correlations as independent normal variables, while zero correlations follow a non‑normal joint distribution, enabling variable importance interpretation. A modified bootstrap method is proposed to quantify uncertainty and assess variable entry, with results validated by simulation and data examples.
By Karl B. Gregory, Daniel J. Nordman
arXiv:2309. 15769v3 Announce Type: replace-cross Abstract: Recent advances in deep learning have highlighted the phenomenon of benign overfitting in overparameterized statistical models, sparking significant interest in understanding its foundations.
By Dennis Shen, Dogyoon Song, Peng Ding, Jasjeet S. Sekhon
arXiv:1812.09632v3 Announce Type: replace
Abstract: We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributi...
By Bal\'azs Csan\'ad Cs\'aji, Kriszti\'an Bal\'azs Kis