Some strong limit theorems for M-estimators

DOI10.1016/0304-4149(94)90066-3zbMath0835.62050OpenAlexW2020632715MaRDI QIDQ1343580

Miguel A. Arcones

Publication date: 21 April 1996

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(94)90066-3

zbMATH Keywords

empirical processesM-estimatorsrates of convergencelaws of the iterated logarithmBahadur-Kiefer representationscubic root asymptoticsTalagrand isoperimetric inequality

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

Related Items (3)

Strong convergence of estimators in nonlinear autoregressive models ⋮ The Bahadur-Kiefer representation for \(U\)-quantiles ⋮ Strong convergence of estimators as \(\varepsilon_n\)-minimisers of optimisation problems

Cites Work

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• Isoperimetry and integrability of the sum of independent Banach-space valued random variables
• The law of the iterated logarithm for \(U\)-processes
• Cube root asymptotics
• Asymptotics for \(M\)-estimators defined by convex minimization
• A strong convergence theorem for Banach space valued random variables
• Distributional convergence of M-estimators under unusual rates
• A general approach to Bahadur-Kiefer representations for \(M\)-estimators
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Approximation Theorems of Mathematical Statistics
• Convergence of stochastic processes

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