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Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals

Published online by Cambridge University Press:  11 February 2009

Masanobu Taniguchi  and
Madan L. Puri
Masanobu Taniguchi
Affiliation:
Osaka University
Madan L. Puri
Affiliation:
Indiana University
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Abstract

Consider a linear regression model y1 = x1β + u1, where the u1'S afe weakly dependent random variables, the x1's are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator βn of) β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for βn is derived. Here we do not assume the normality of (u1), and (u1) includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(βn) of βn. Then, a sufficient condition for T to extinguish the second-order terms is given. The results are applicable to many statistical problems.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 2 , June 1996 , pp. 331 - 346
Copyright
Copyright © Cambridge University Press 1996

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References

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