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Two-term Edgeworth expansion for M-estimators of a linear regression parameter without Cramér-type conditions and an application to the bootstrap

Part of: Linear inference, regression Parametric inference

Published online by Cambridge University Press:  09 April 2009

I. Karabulut  and
S. N. Lahiri
I. Karabulut
Affiliation:
Department of Statistics Gasi UniversityAnkara, Trukey
S. N. Lahiri
Affiliation:
Department of Statistics Iowa State UniversityAmes, Iowa 50011, USA
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Abstract

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A two-term Edgeworth expansion for the distribution of an M-estimator of a simple linear regression parameter is obtained without assuming any Cramér-type conditions. As an application, it is shown that certain modification of the naive bootstrap procedure is second order correct even when the error variables have a lattice distribution. This is in marked contrast with the results of Singh on the sample mean of independent and identically distributed random variables.

Keywords

BootstrapCramérs conditionEdgeworth expansionM-estimatorsregression

MSC classification

Secondary: 62F12: Asymptotic properties of estimators 62J05: Linear regression
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 361 - 370
Copyright
Copyright © Australian Mathematical Society 1997

References

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