Valid edgeworth expansions of M-estimators in regression models with weakly dependent residuals

Masanobu Taniguchi, Madan L. Puri

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Abstract

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

Original languageEnglish
Pages (from-to)331-346
Number of pages16
JournalEconometric Theory
Volume12
Issue number2
Publication statusPublished - 1996
Externally publishedYes

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ASJC Scopus subject areas

  • Economics and Econometrics
  • Social Sciences (miscellaneous)

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