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: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
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:2608. 07281v1 Announce Type: cross Abstract: This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally.
By Zhijun Liu, Dandan Jiang
arXiv:2509. 03758v5 Announce Type: replace Abstract: We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations.
By Alvaro Almeida Gomez
arXiv:2411.02771v3 Announce Type: replace-cross
Abstract: Doubly robust estimators are widely used for estimating average treatment effects and other linear summaries of regression functions. While c...
By Lars van der Laan, Alex Luedtke, Marco Carone