scholarly journals Convergence Rates of Density Estimation in Besov Spaces

2011 ◽  
Vol 02 (10) ◽  
pp. 1258-1262 ◽  
Author(s):  
Huiying Wang
Keyword(s):  
Density Estimation ◽  
Besov Spaces ◽  
Convergence Rates

A note on wavelet deconvolution density estimation

2017 ◽  
Vol 15 (06) ◽  
pp. 1750055 ◽  
Author(s):  
Xiaochen Zeng
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Density Estimation ◽  
Besov Spaces ◽  
One Dimensional ◽  
Bounded Set ◽  
Multivariate Density Estimation ◽  
Free Case ◽  
Ill Posed ◽  
Multivariate Density

This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Giné and Nickl’s (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry’s theorem (Stoch. Process. Appl., 1997) to some extent.

Density estimation by kernel and wavelets methods: Optimality of Besov spaces

1993 ◽  
Vol 18 (4) ◽  
pp. 327-336 ◽  
Author(s):  
Gérard Kerkyacharian ◽  
Dominique Picard
Keyword(s):  
Density Estimation ◽  
Besov Spaces

Sup-norm convergence rates for Lévy density estimation

Extremes ◽  
2016 ◽  
Vol 19 (3) ◽  
pp. 371-403 ◽  
Author(s):  
Valentin Konakov ◽  
Vladimir Panov
Keyword(s):  
Density Estimation ◽  
Convergence Rates ◽  
Norm Convergence ◽  
Lévy Density

The Lower Bound of Density Estimation for Biased Data in Sobolev Spaces

2013 ◽  
Vol 765-767 ◽  
pp. 744-748
Author(s):  
Jin Ru Wang ◽  
Yuan Zhou
Keyword(s):  
Lower Bound ◽  
Density Estimation ◽  
Sobolev Spaces ◽  
Convergence Rates ◽  
Estimation Problem ◽  
Independent And Identically Distributed

In this paper, we consider the density estimation problem from independent and identically distributed (i.i.d.) biased observations. We study the lower bound of convergence rates of density estimation over Sobolev spaces WrN(NN+) under the Lp risk by using Fanos lemma.

Density estimation in Besov spaces

1992 ◽  
Vol 13 (1) ◽  
pp. 15-24 ◽  
Author(s):  
G. Kerkyacharian ◽  
D. Picard
Keyword(s):  
Density Estimation ◽  
Besov Spaces

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.

Sign in / Sign up

Export Citation Format

Share Document