scholarly journals Lower bounds in the convolution structure density model

Bernoulli ◽  
2017 ◽  
Vol 23 (2) ◽  
pp. 884-926 ◽  
Author(s):  
O.V. Lepski ◽  
T. Willer
Keyword(s):  
Lower Bounds ◽  
Density Model ◽  
Convolution Structure ◽  
Structure Density

scholarly journals Adaptive Wavelet Estimations in the Convolution Structure Density Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1391
Author(s):  
Kaikai Cao ◽  
Xiaochen Zeng
Keyword(s):  
Kernel Methods ◽  
Convergence Rates ◽  
Adaptive Estimation ◽  
Density Model ◽  
Oracle Inequalities ◽  
Adaptive Wavelet ◽  
Wavelet Estimator ◽  
Convolution Structure ◽  
Optimal Convergence Rates ◽  
Structure Density

Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal Lp risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat.2019, 47, 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds
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