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.
Bibliographical noteFunding Information:
The work was partly supported by the U.S. National Institute of Education.
- Combining information
- Linear combination of estimators
- Weighted mean