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

Masanobu Taniguchi and Madan L. Puri

Econometric Theory, 1996, vol. 12, issue 2, 331-346

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.

Date: 1996
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