The variance of a linear combination of independent estimators using estimated weights

Donald B. Rubin; Sanford Weisberg

doi:10.1093/biomet/62.3.708

The variance of a linear combination of independent estimators using estimated weights

Donald B. Rubin, Sanford Weisberg

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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)
Pages (from-to)	708-709
Number of pages	2
Journal	Biometrika
Volume	62
Issue number	3
DOIs	https://doi.org/10.1093/biomet/62.3.708
State	Published - Dec 1975

Bibliographical note

Funding Information:
The work was partly supported by the U.S. National Institute of Education.

Keywords

Combining information
Linear combination of estimators
Weighted mean

Publisher link

10.1093/biomet/62.3.708

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title = "The variance of a linear combination of independent estimators using estimated weights",

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.",

keywords = "Combining information, Linear combination of estimators, Weighted mean",

author = "Rubin, {Donald B.} and Sanford Weisberg",

note = "Funding Information: The work was partly supported by the U.S. National Institute of Education.",

year = "1975",

month = dec,

doi = "10.1093/biomet/62.3.708",

language = "English (US)",

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pages = "708--709",

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T1 - The variance of a linear combination of independent estimators using estimated weights

AU - Rubin, Donald B.

AU - Weisberg, Sanford

N1 - Funding Information: The work was partly supported by the U.S. National Institute of Education.

PY - 1975/12

Y1 - 1975/12

N2 - 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.

AB - 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.

KW - Combining information

KW - Linear combination of estimators

KW - Weighted mean

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JO - Biometrika

JF - Biometrika

IS - 3

ER -

The variance of a linear combination of independent estimators using estimated weights

Abstract

Bibliographical note

Keywords

Publisher link

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