Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals
研究了线性回归模型中M估计量的二阶Edgeworth展开，不要求残差正态性，适用于ARMA等弱相依过程，并给出了消除二阶项的变换条件。
Consider a linear regression model y 1 = x 1 β + u 1 , where the u 1 'S afe weakly dependent random variables, the x 1 '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 1 ), and (u 1 ) includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(βn) 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.