### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Probability Theory and Extreme Value Theory*(Vol. 2, pp. 517-532). De Gruyter Mouton.