On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise-Reference-Cited by-同舟云学术

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

Published:2019-12-01 Issue:6 Volume:69 Page:1485-1500
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Yu Yuncai¹,Liu Xinsheng¹,Liu Ling²,Liu Weisi¹

Affiliation:

1. State Key Laboratory of Mechanics and Control of Mechanical Structures , Institute of Nano Science and Department of Mathematics Nanjing University of Aeronautics and Astronautics , Nanjing , China

2. Department of Information Science and Technology , Donghua University , Shanghai , China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0324/pdf

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