Optimal Rates of Convergence for Deconvolving a Density

1988 ◽  
Author(s):  
Raymond J. Carroll ◽  
Peter Hall
Keyword(s):  
Rates Of Convergence ◽  
Optimal Rates Of Convergence

scholarly journals BLOCK THRESHOLDING FOR A DENSITY ESTIMATION PROBLEM WITH A CHANGE-POINT

2009 ◽  
Vol 02 (04) ◽  
pp. 545-555 ◽  
Author(s):  
Christophe Chesneau
Keyword(s):  
Density Estimation ◽  
Change Point ◽  
General Framework ◽  
Rates Of Convergence ◽  
Estimation Problem ◽  
Adaptive Estimator ◽  
Function Classes ◽  
Wide Range ◽  
Optimal Rates Of Convergence ◽  
Block Thresholding

We consider a density estimation problem with a change-point. The contribution of the paper is theoretical: we develop an adaptive estimator based on wavelet block thresholding and we evaluate these performances via the minimax approach under the 𝕃p risk with p ≥ 1 over a wide range of function classes: the Besov classes, [Formula: see text] (with no particular restriction on the parameters π and r). Under this general framework, we prove that it attains near optimal rates of convergence.

scholarly journals Optimal rates of convergence for covariance matrix estimation

2010 ◽  
Vol 38 (4) ◽  
pp. 2118-2144 ◽  
Author(s):  
T. Tony Cai ◽  
Cun-Hui Zhang ◽  
Harrison H. Zhou
Keyword(s):  
Covariance Matrix ◽  
Rates Of Convergence ◽  
Covariance Matrix Estimation ◽  
Matrix Estimation ◽  
Optimal Rates Of Convergence
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