Valid Edgeworth expansions of M-Estimators in regression models with weakly dependent residuals

Masanobu Taniguchi, Madan L. Puri

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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

Original languageEnglish
Title of host publicationProbability Theory and Extreme Value Theory
PublisherDe Gruyter Mouton
Pages517-532
Number of pages16
Volume2
ISBN (Electronic)9783110917826
ISBN (Print)9789067643856
Publication statusPublished - 2011 Jul 11
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Taniguchi, M., & Puri, M. L. (2011). Valid Edgeworth expansions of M-Estimators in regression models with weakly dependent residuals. In Probability Theory and Extreme Value Theory (Vol. 2, pp. 517-532). De Gruyter Mouton.