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Empirical Processes in M-Estimation.rar
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EmpiricalProcessesinM-Estimation

by
SaravandeGeer

Handoutat NewDirectionsinGeneralEquilibriumAnalysis
CowlesWorkshop,YaleUniversity
June15-20,2003Version:June13,2003

Contents
Part1
EmpiricalprocessesandasymptoticnormalityofM-estimators
1.Introduction
1.1.Lawoflargenumbersforreal-valuedrandomvariables
1.2. Rd-valuedrandomvariables
1.3.DefinitionGlivenko-Cantelliclassesofsets.
2.WhichclassesareGlivenko-Cantelliclasses?
2.1.GeneralGlivenko-Cantelliclasses
2.2.Vapnik-Chervonenkisclasses
3.Convergenceofmeanstotheirexpectations
3.1.Uniformlawoflargenumbersforclassesoffunctions
3.2.VCclassesoffunctions
3.3.Exercises
4.Uniformcentrallimittheorems
4.1.Real-valuedrandomvariables
4.2. Rd-valuedrandomvariables
4.3.Donsker’stheorem
4.4.Donskerclasses
5.M-estimators
5.1.WhatisanM-estimator?
5.2.Consistencyanduniformlawsoflargenumbers
5.3.AsymptoticnormalityofM-estimators
……

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