Minimax estimation of linear functionals over nonconvex parameter spaces.

DOI10.1214/009053604000000094zbMath1048.62054arXivmath/0406427OpenAlexW3099874003MaRDI QIDQ1879943

T. Tony Cai, Mark G. Low

Publication date: 15 September 2004

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

Full work available at URL: https://arxiv.org/abs/math/0406427

zbMATH Keywords

modulus of continuitylinear functionalsminimax estimationwhite noise modelnonparametric functional estimationconstrained risk inequality

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Minimax procedures in statistical decision theory (62C20) Inference from stochastic processes (62M99) Nonparametric inference (62G99)

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Cites Work

• Geometrizing rates of convergence. II
• Geometrizing rates of convergence. III
• Adaptive estimates of linear functionals
• Statistical estimation and optimal recovery
• A constrained risk inequality with applications to nonparametric functional estimation
• Non-asymptotic minimax rates of testing in signal detection
• Bias-variance tradeoffs in functional estimation problems
• Adapting to unknown sparsity by controlling the false discovery rate
• On Nonparametric Estimation of the Value of a Linear Functional in Gaussian White Noise
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