scholarly journals Convergence rates for posterior distributions and adaptive estimation

2004 ◽  
Vol 32 (4) ◽  
pp. 1556-1593 ◽  
Author(s):  
Tzee-Ming Huang
Keyword(s):  
Convergence Rates ◽  
Adaptive Estimation ◽  
Posterior Distributions

scholarly journals Convergence rates of variational posterior distributions

2020 ◽  
Vol 48 (4) ◽  
pp. 2180-2207 ◽  
Author(s):  
Fengshuo Zhang ◽  
Chao Gao
Keyword(s):  
Convergence Rates ◽  
Posterior Distributions

scholarly journals Convergence rates of posterior distributions for noniid observations

2007 ◽  
Vol 35 (1) ◽  
pp. 192-223 ◽  
Author(s):  
Subhashis Ghosal ◽  
Aad van der Vaart
Keyword(s):  
Convergence Rates ◽  
Posterior Distributions

A note on convergence rates for posterior distributions via large deviations techniques

2008 ◽  
Vol 51 (2) ◽  
pp. 337-347
Author(s):  
Andrea Martinelli ◽  
Matteo Ruggiero ◽  
Stephen G. Walker
Keyword(s):  
Large Deviations ◽  
Convergence Rates ◽  
Posterior Distributions

scholarly journals Convergence rates of posterior distributions for Brownian semimartingale models

Bernoulli ◽  
2006 ◽  
Vol 12 (5) ◽  
pp. 863-888 ◽  
Author(s):  
F.H. Van Der Meulen ◽  
Aad W. Van Der Vaart ◽  
J.H. Van Zanten
Keyword(s):  
Convergence Rates ◽  
Posterior Distributions

ON CONVERGENCE RATES FOR NONPARAMETRIC POSTERIOR DISTRIBUTIONS

2007 ◽  
Vol 49 (3) ◽  
pp. 209-219
Author(s):  
Antonio Lijoi ◽  
Igor Prünster ◽  
Stephen G. Walker
Keyword(s):  
Convergence Rates ◽  
Posterior Distributions

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.

Strong Lp convergence of wavelet deconvolution density estimators

2018 ◽  
Vol 16 (02) ◽  
pp. 183-208 ◽  
Author(s):  
Youming Liu ◽  
Xiaochen Zeng
Keyword(s):  
Limit Theorems ◽  
Convergence Rates ◽  
Adaptive Estimation ◽  
Uniform Limit ◽  
Spline Wavelets ◽  
Noise Density ◽  
Ill Posed ◽  
The Fourier Transform ◽  
Wavelet Estimators ◽  
Density Estimators

Using compactly supported wavelets, Giné and Nickl [Uniform limit theorems for wavelet density estimators, Ann. Probab. 37(4) (2009) 1605–1646] obtain the optimal strong [Formula: see text] convergence rates of wavelet estimators for a fixed noise-free density function. They also study the same problem by spline wavelets [Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections, Bernoulli 16(4) (2010) 1137–1163]. This paper considers the strong [Formula: see text] convergence of wavelet deconvolution density estimators. We first show the strong [Formula: see text] consistency of our wavelet estimator, when the Fourier transform of the noise density has no zeros. Then strong [Formula: see text] convergence rates are provided, when the noises are severely and moderately ill-posed. In particular, for moderately ill-posed noises and [Formula: see text], our convergence rate is close to Giné and Nickl’s.

scholarly journals Convergence rates of posterior distributions

2000 ◽  
Vol 28 (2) ◽  
pp. 500-531 ◽  
Author(s):  
Subhashis Ghosal ◽  
Jayanta K. Ghosh ◽  
Aad W. van der Vaart
Keyword(s):  
Convergence Rates ◽  
Posterior Distributions
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