Minimax exact constant in sup-norm for nonparametric regression with random design

DOI10.1016/S0378-3758(03)00154-XzbMath1045.62029MaRDI QIDQ1877833

Karine Bertin

Publication date: 19 August 2004

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

zbMATH Keywords

normUniformMinimax exact constantMinimax risk

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Minimax procedures in statistical decision theory (62C20)

Related Items (6)

A sup-norm oracle inequality for a partially linear regression model ⋮ Sharp optimality for regression with real-time data ⋮ MinimumL_pNorm Estimator for Simple Linear Regressive Model ⋮ Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes ⋮ Sharp estimation in sup norm with random design ⋮ Adaptive density estimation on bounded domains

Cites Work

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• Nonparametric curve estimation. Methods, theory, and applications
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• Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point
• Optimal global rates of convergence for nonparametric regression
• The asymptotic minimax constant for sup-norm loss in nonparametric density estimation
• Bounds for the Risks of Non-Parametric Regression Estimates
• An Asymptotically Minimax Regression Estimator in the Uniform Norm up to Exact Constant

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