Minimax estimation via wavelets for indirect long-memory data

DOI10.1016/S0378-3758(96)00205-4zbMath0890.62031MaRDI QIDQ1372865

Yazhen Wang

Publication date: 22 June 1998

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

zbMATH Keywords

fractional Brownian motionlong-range dependencelinear inverse problemsminimax risksfractional Gaussian noise modelwavelet-vaguelette decompositions

Mathematics Subject Classification ID

Density estimation (62G07) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Minimax procedures in statistical decision theory (62C20)

Related Items (15)

Deconvolution model with fractional Gaussian noise: a minimax study ⋮ Minimax lower bounds for the simultaneous wavelet deconvolution with fractional Gaussian noise and unknown kernels ⋮ Minimax estimation of linear functionals under squared error loss ⋮ Laplace deconvolution with dependent errors: a minimax study ⋮ Blind deconvolution model in periodic setting with fractional Gaussian noise ⋮ Anisotropic functional deconvolution for the irregular design: A minimax study ⋮ Thresholding estimators for linear inverse problems and deconvolutions ⋮ Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series ⋮ Wavelet deconvolution in a periodic setting with long-range dependent errors ⋮ Wavelet estimation of function derivatives from a multichannel deconvolution model ⋮ Multichannel deconvolution with long-range dependence: a minimax study ⋮ Kink estimation with correlated noise ⋮ Multiscale density estimation with errors in variables ⋮ Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet ⋮ Multichannel deconvolution with long range dependence: upper bounds on the \(L^p\)-risk \((1 \leq p < \infty)\)

Cites Work

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• Asymptotic equivalence of nonparametric regression and white noise
• Function estimation via wavelet shrinkage for long-memory data
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• Ten Lectures on Wavelets
• Entropy Numbers and Approximation Numbers in Function Spaces, II
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Fractional Brownian Motions, Fractional Noises and Applications

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