Life sciences · Preprint

Optimal estimation for Functional Linear Regression with Noisy Discretized Data

arXiv · September 8, 2026

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AI Summary

This is a mathematical and statistical methods paper proposing a two-step procedure for scalar-on-function linear regression from noisy discretized functional data. The authors establish theoretical convergence rates and minimax optimality under regularity assumptions, with illustration on simulated and meteorological data, but provide no clinical validation, comparative efficacy, or evidence of practical advantage.

What was studied

Preprint.

Key findings

Oracle-type inequalities established for prediction error with respect to reconstructed and true latent curves Convergence rates derived showing minimax optimality when number of grid points is sufficiently large Method illustrated on simulated data and one real meteorological dataset

Safety

Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.

Who this may help

The source did not state who this applies to in practice.

Plain-language summary

This is a methodological paper proposing a statistical estimation procedure with theoretical analysis but no clinical application, comparative validation, or empirical performance benchmarking against existing methods.

Caveats

Work has not been peer reviewed; posted on arXiv as preprint only
No numerical performance metrics, comparison to alternative methods, or effect sizes reported in abstract
Real data example is meteorological, not biomedical or clinical in nature
Theoretical results conditional on unspecified regularity assumptions and polynomial eigenvalue decay

Evidence assessment

Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.

Study design

insufficient

No empirical study design; theoretical development with simulation and one observational dataset.

Directness

insufficient

No clinical or biomedical application stated; purely statistical methodology paper.

Consistency

insufficient

No comparison to other methods or prior work reported in the abstract.

Risk of bias

insufficient

Not applicable to theoretical methodological work; no randomization or blinding.

Sample adequacy

insufficient

Simulated data only; real data application is one meteorological dataset of unspecified size.

What is missing. This record has no reported figures. That is a gap in the analysis, not a judgement about the study.

Source abstract

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. Under regularity assumptions on the slope function and polynomial decay of the eigenvalues of the covariate, we derive convergence rates for the prediction error and show that our estimator attains the minimax rate when the number of grid points is sufficiently large. Finally, the proposed method is illustrated on simulated data and on a real meteorological dataset.

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