Adaptive estimation of an additive regression function from weakly dependent data

TL;DR

This paper introduces an adaptive wavelet-based estimator for additive regression functions with dependent data, achieving optimal convergence rates similar to independent data scenarios.

Contribution

It develops a new estimator using marginal integration and wavelets for dependent data, with proven optimal asymptotic properties under the minimax framework.

Findings

Attains sharp convergence rates matching iid cases.

Effective for high-dimensional additive models.

Provides theoretical guarantees under dependence.

Abstract

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive regression function. Its asymptotic properties are investigated via the minimax approach under the $\mathbb{L}_2$ risk over Besov balls. We prove that it attains a sharp rate of convergence which turns to be the one obtained in the $\iid$ case for the standard univariate regression estimation problem.