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.
|Title of host publication||Probability Theory and Extreme Value Theory|
|Publisher||De Gruyter Mouton|
|Number of pages||16|
|Publication status||Published - 2011 Jul 11|
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