On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise

TL;DR

This paper studies wavelet thresholding estimators in nonparametric regression with negatively super-additive dependent noise, showing they achieve optimal convergence rates and are adaptive, supported by numerical simulations.

Contribution

It demonstrates that thresholding estimators remain effective and adaptive under NSD noise, achieving optimal convergence rates over Besov spaces.

Findings

Term-by-term thresholding estimator nearly optimal

Block thresholding estimator achieves optimal rates

Numerical simulations confirm estimator validity and adaptivity

Abstract

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.