SOURCE-LINKED INTELLIGENCE

Optimal estimation for Functional Linear Regression with Noisy Discretized Data

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

In this paper, we consider the scalar-on-function linear regression model under a realistic sampling scheme in which the functional covariates are observed on a regular grid and contaminated by additive noise. We propose a two-step estimation procedure: first, the underlying curves are reconstructed from the discrete noisy observations using a Fourier-based projection method; second, the slope function is estimated by a penalized least-squares criterion over finite-dimensional trigonometric spaces, with data-driven selection of the model dimension. We establish oracle-type inequalities for the

Read original source ↗ Open in workspace

recordType

paper

region

Global