Deconvolution with unknown error distribution

DOI10.1214/08-AOS652zbMath1173.62018arXiv0705.3482MaRDI QIDQ834341

Jan Johannes

Publication date: 19 August 2009

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.3482

zbMATH Keywords

Fourier transformSobolev spacekernel estimationdeconvolutionoptimal rate of convergencesource conditionRosenblatt-Parzen kernel estimatorspectral cut off

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

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Cites Work

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• Density deconvolution in the circular structural model
• On the optimal rates of convergence for nonparametric deconvolution problems
• Regularization of ill-posed problems by stochastic iteration procedures in the mean
• Rates of convergence of some estimators in a class of deconvolution problems
• Inference in components of variance models with low replication
• Adaptive wavelet estimator for nonparametric density deconvolution
• Optimal spherical deconvolution
• Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model
• Fourier methods for estimating mixing densities and distributions
• On pointwise adaptive nonparametric deconvolution
• Deconvolution from panel data with unknown error distribution
• Log-density Deconvolution by Wavelet Thresholding
• Regularization in Hilbert scales under general smoothing conditions
• Penalized contrast estimator for adaptive density deconvolution
• Optimal Rates of Convergence for Deconvolving a Density
• Deconvolution with supersmooth distributions
• Asymptotic Statistics
• Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
• On the effect of estimating the error density in nonparametric deconvolution
• B-Spline deconvolution based on the Em algorithm
• Density Estimation for the Case of Supersmooth Measurement Error
• Wavelet deconvolution
• Statistical Inverse Estimation in Hilbert Scales
• Consistent deconvolution in density estimation
• Error bounds for tikhonov regularization in hilbert scales
• Semiparametric Estimation of Regression Models for Panel Data
• Error Estimates for Regularization Methods in Hilbert Scales
• Discrete-transform approach to deconvolution problems
• Adaptive estimation for inverse problems with noisy operators
• On Estimation of a Probability Density Function and Mode

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