Minimax wavelet estimation for multisample heteroscedastic non-parametric regression

TL;DR

This paper develops a wavelet-based minimax estimation method for multisample heteroscedastic non-parametric regression, providing theoretical bounds and demonstrating effectiveness on simulated and real data.

Contribution

It introduces the first theoretical minimax results for multisample non-parametric regression with irregular signals using wavelet estimators.

Findings

Established lower and upper bounds for minimax risk.

Proposed a wavelet estimator achieving optimal rates.

Validated approach on simulated and experimental datasets.

Abstract

The problem of estimating the baseline signal from multisample noisy curves is investigated. We consider the functional mixed effects model, and we suppose that the functional fixed effect belongs to the Besov class. This framework allows us to model curves that can exhibit strong irregularities, such as peaks or jumps for instance. The lower bound for the $L_2$ minimax risk is provided, as well as the upper bound of the minimax rate, that is derived by constructing a wavelet estimator for the functional fixed effect. Our work constitutes the first theoretical functional results in multisample non parametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data.