### Abstract

SUMMARY: Consider k independent unbiased estimators of a common parameter τ. Let t^{*} be the linear combination of the k estimators with minimum variance, and let t∩ be any linear combination whose weights sum to unity and are independent of the k estimators. Then t∩ is unbiased for τ and the variance of t∩ depends only on the variance of t^{*} and the mean squared error of the weights as estimates of the optimum weights.

Original language | English (US) |
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Pages (from-to) | 708-709 |

Number of pages | 2 |

Journal | Biometrika |

Volume | 62 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1975 |

### Keywords

- Combining information
- Linear combination of estimators
- Weighted mean

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## Cite this

Rubin, D. B., & Weisberg, S. (1975). The variance of a linear combination of independent estimators using estimated weights.

*Biometrika*,*62*(3), 708-709. https://doi.org/10.1093/biomet/62.3.708