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 language | English |
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Title of host publication | Probability Theory and Extreme Value Theory |
Publisher | De Gruyter Mouton |
Pages | 517-532 |
Number of pages | 16 |
Volume | 2 |
ISBN (Electronic) | 9783110917826 |
ISBN (Print) | 9789067643856 |
Publication status | Published - 2011 Jul 11 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)