On mean estimation for heteroscedastic random variables

DOI10.1214/21-AIHP1239MaRDI QIDQ2686600

Gábor Lugosi, Nikita Zhivotovskiy, Silvio Lattanzi, Luc P. Devroye

Publication date: 28 February 2023

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.11537

zbMATH Keywords

robustnessadaptivityorder statisticmean estimationheteroscedastic observations

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Robustness and adaptive procedures (parametric inference) (62F35) Order statistics; empirical distribution functions (62G30)

Cites Work

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• Rate of convergence to the normal law of order statistics for nonidentically distributed random variables
• Robust estimation in models for independent non-identically distributed data
• Robust estimation in heteroscedastic linear models
• Estimation for a linear regression model with unknown diagonal covariance matrix
• Sphere packing numbers for subsets of the Boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension
• Time bounds for selection
• Necessary and sufficient conditions for weak consistency of the median of independent but not identically distributed random variables
• Non-asymptotic bounds for percentiles of independent non-identical random variables
• Estimation of the mode
• Local Rademacher complexities
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• On the minimum of several random variables
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• Local Asymptotic Normality for Non-Identically Distributed Observations
• Fast classification rates without standard margin assumptions
• Learning Entangled Single-Sample Gaussians