Optimal estimation for Functional Linear Regression with Noisy Discretized Data
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 prediction error, both with respect to the reconstructed curves and to the true latent curves. U...
| Authors | Sixtine Sphabmixay |
|---|---|
| Primary category | stat.ML |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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