### 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.

**Valid edgeworth expansions of M-estimators in regression models with weakly dependent residuals.** / Taniguchi, Masanobu; Puri, Madan L.

Research output: Contribution to journal › Article

*Econometric Theory*, vol. 12, no. 2, pp. 331-346.

}

TY - JOUR

T1 - Valid edgeworth expansions of M-estimators in regression models with weakly dependent residuals

AU - Taniguchi, Masanobu

AU - Puri, Madan L.

PY - 1996

Y1 - 1996

N2 - Consider a linear regression model yt = xtβ + ut, where the ut's are weakly dependent random variables, the xt's are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator β̂n of β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for β̂n is derived. Here we do not assume the normality of {ut}, and {ut} includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(β̂n) of β̂n. Then, a sufficient condition for T to extinguish the second-order terms is given. The results are applicable to many statistical problems.

AB - Consider a linear regression model yt = xtβ + ut, where the ut's are weakly dependent random variables, the xt's are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator β̂n of β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for β̂n is derived. Here we do not assume the normality of {ut}, and {ut} includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(β̂n) of β̂n. Then, a sufficient condition for T to extinguish the second-order terms is given. The results are applicable to many statistical problems.

UR - http://www.scopus.com/inward/record.url?scp=0030541391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030541391&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 331

EP - 346

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 2

ER -