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Biometrika 1975 62(3):708-709; doi:10.1093/biomet/62.3.708
© 1975 by Biometrika Trust
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The variance of a linear combination of independent estimators using estimated weights

DONALD B. RUBIN and SANFORD WEISBERG

Educational Testing Service Princeton
Department of Applied Statistics, University of Minnesota Twin Cities

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

Key Words: Combining information • Linear combination of estimators • Weighted mean


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