### 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 β̂_{n} of β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for β̂_{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(β̂_{n}) of β̂_{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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Pages (from-to) | 331-346 |

Number of pages | 16 |

Journal | Econometric Theory |

Volume | 12 |

Issue number | 2 |

Publication status | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Economics and Econometrics
- Social Sciences (miscellaneous)

### Cite this

*Econometric Theory*,

*12*(2), 331-346.