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

Donald B. Rubin, Sanford Weisberg

Research output: Contribution to journalArticle

6 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 languageEnglish (US)
Pages (from-to)708-709
Number of pages2
JournalBiometrika
Volume62
Issue number3
DOIs
StatePublished - Dec 1975

Keywords

  • Combining information
  • Linear combination of estimators
  • Weighted mean

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