VALID EDGEWORTH EXPANSIONS OF M-ESTIMATORS IN REGRESSION MODELS WITH WEAKLY DEPENDENT RESIDUALS
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説明
<jats:p>Consider a linear regression model y<jats:sub>1</jats:sub> = x<jats:sub>1</jats:sub>β + u<jats:sub>1</jats:sub>, where the u<jats:sub>1</jats:sub>'S afe weakly dependent random variables, the x<jats:sub>1</jats:sub>'s are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator β<jats:sub>n</jats:sub> of) β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for β<jats:sub>n</jats:sub> is derived. Here we do not assume the normality of (u<jats:sub>1</jats:sub>), and (u<jats:sub>1</jats:sub>) includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(βn) of β<jats:sub>n</jats:sub>. Then, a sufficient condition for <jats:italic>T</jats:italic> to extinguish the second-order terms is given. The results are applicable to many statistical problems.</jats:p>
収録刊行物
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- Econometric Theory
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Econometric Theory 12 331-346, 1996-06-01
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