A central limit theorem applicable to robust regression estimators

DOI10.1016/0047-259X(87)90073-XzbMath0626.62033MaRDI QIDQ580843

Stephen L. Portnoy

Publication date: 1987

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

central limit theoremrobust regression estimatorsgeneral linear modelasymptotic normal approximationrobust M-estimatorstrong normal approximation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Linear regression; mixed models (62J05) Central limit and other weak theorems (60F05) Robustness and adaptive procedures (parametric inference) (62F35)

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Cites Work

• Unnamed Item
• Asymptotic behavior of M-estimators of p regression parameters when \(p^ 2/n\) is large. I. Consistency
• Asymptotic behavior of M estimators of p regression parameters when \(p^ 2/n\) is large. II: Normal approximation
• Asymptotic behavior of M-estimators for the linear model
• Robust regression: Asymptotics, conjectures and Monte Carlo
• On Interchanging Limits and Integrals
• Uniform Estimates of the Rate of Convergence in the Multi-Dimensional Central Limit Theorem
• Robust Statistics