scholarly journals Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces

2020 ◽  
Vol 58 (1) ◽  
pp. 21-47 ◽  
Author(s):  
Frederic Weidling ◽  
Benjamin Sprung ◽  
Thorsten Hohage
Keyword(s):  
Tikhonov Regularization ◽  
Besov Spaces ◽  
Convergence Rates ◽  
Optimal Convergence ◽  
Optimal Convergence Rates

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

2019 ◽  
Vol 69 (6) ◽  
pp. 1485-1500 ◽  
Author(s):  
Yuncai Yu ◽  
Xinsheng Liu ◽  
Ling Liu ◽  
Weisi Liu
Keyword(s):  
Regression Model ◽  
Numerical Simulations ◽  
Nonparametric Regression ◽  
Besov Spaces ◽  
Convergence Rates ◽  
Wavelet Thresholding ◽  
Nonparametric Regression Model ◽  
Optimal Convergence ◽  
Optimal Convergence Rates ◽  
Block Thresholding

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.

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