Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes

DOI10.3150/bj/1099579160zbMath1103.62078OpenAlexW2091459303MaRDI QIDQ1769787

Karine Bertin

Publication date: 30 March 2005

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3150/bj/1099579160

zbMATH Keywords

uniform normwhite noise modelanisotropic Hölder classminimax exact constant

Mathematics Subject Classification ID

Non-Markovian processes: estimation (62M09) Markov processes: estimation; hidden Markov models (62M05) Applications of functional analysis in probability theory and statistics (46N30)

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Maxiset in sup-norm for kernel estimators ⋮ Minimax nonparametric estimation on maxisets ⋮ Fast adaptive estimation of log-additive exponential models in Kullback-Leibler divergence ⋮ Structural adaptation via \(\mathbb L_p\)-norm oracle inequalities ⋮ Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach ⋮ Sharp estimation in sup norm with random design ⋮ Universal pointwise selection rule in multivariate function estimation ⋮ Nonparametric estimation of composite functions ⋮ Sup-norm adaptive drift estimation for multivariate nonreversible diffusions

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