### Abstract

The aim of this study is to improve the e0ciency of weighted least-squares estimates for a regression parameter. An iterative procedure, starting with an unbiased estimate other than the unweighted least-squares estimate, yields estimates which are asymptotically more e0cient than the feasible generalized least-squares estimate when errors are spherically distributed. The result has an application in the improvement of the Graybill-Deal estimate of the common mean of several normal populations.

Original language | English |
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Pages (from-to) | 133-146 |

Number of pages | 14 |

Journal | Journal of Statistical Planning and Inference |

Volume | 110 |

Issue number | 1-2 |

Publication status | Published - 2003 Jan 15 |

Externally published | Yes |

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### Keywords

- Asymptotic variance
- Common mean
- Graybill-Deal estimate
- Heteroscedastic linear regression
- Iterative procedure
- Replication
- Spherical distribution

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability