Some strong limit theorems for M-estimators
type: Item
instance of: scholarly article
title: Some strong limit theorems for M-estimators
zbMATH Open document ID: 0835.62050
DOI: 10.1016/0304-4149(94)90066-3
author: Miguel A. Arcones
published in: Stochastic Processes and their Applications
publication date: 1996-04-21T00:00:00Z
review text: Using the Talagrand isoperimetric inequality, the author establishes some laws of the iterated logarithm for empirical processes rescaled in the ``time'' parameter. These laws are applied to obtain the LIL for \(M\)- estimators with unusual rates of convergence (in particular, with cubic root asymptotics instead of the usual rate \(((n/2) \log \log n)^{1/2})\). Some Bahadur-Kiefer representations for \(M\)-estimators are also given even when the rate is not the standard one.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 713905
zbMATH Keywords: M-estimators
zbMATH Keywords: Talagrand isoperimetric inequality
zbMATH Keywords: laws of the iterated logarithm
zbMATH Keywords: empirical processes
zbMATH Keywords: rates of convergence
zbMATH Keywords: cubic root asymptotics
zbMATH Keywords: Bahadur-Kiefer representations
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90066-3
OpenAlex ID: W2020632715
cites work: Q4001807
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description: scientific article; zbMATH DE number 713905